Beginning Algebra
Purpose of Course showclose
In this course, you will study basic algebraic operations and concepts, as well as the structure and use of algebra. This includes solving algebraic equations, factoring algebraic expressions, working with rational expressions, and graphing linear equations. You will apply these skills to solve realworld problems (word problems). Each unit will have its own application problems, depending on the concepts you have been exposed to. This course is also intended to provide you with a strong foundation for intermediate algebra and beyond. It will begin with a review of some math concepts formed in prealgebra, such as ordering operations and simplifying simple algebraic expressions, to get your feet wet. You will then build on these concepts by learning more about functions, graphing of functions, evaluation of functions, and factorization. You will spend time on the rules of exponents and their applications in distribution of multiplication over addition/subtraction.
This course provides students the opportunity to earn actual college credit. It has been reviewed and recommended for 3 credit hours by The National College Credit Recommendation Service (NCCRS). While credit is not guaranteed at all schools, we have partnered with a number of schools who have expressed their willingness to accept transfer of credits earned through Saylor. You can read more about our NCCRS program here.
Course Information showclose
Course Designer: Frank Appiah and Mark Arnold
Primary Resources: This course is composed of a range of different free, online materials. The core of this course makes use of all the materials originally structured by the Washington State Board for Community and Technical Colleges. In particular, this course uses the following:
 Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition (PDF)
 Tyler Wallace’s Beginning Algebra Lab Notebook (PDF)
 Unit 1 Assignments
 Unit 1 Practice Test
 Unit 2 Assignments
 Unit 2 Practice Test
 Unit 3 Assignments
 Unit 3 Practice Test
 Unit 4 Assignments
 Unit 4 Practice Test
 Unit 5 Assignments
 Unit 5 Practice Test
 Final Exam
In order to “pass” this course, you will need to earn a 70% or higher on the timed, twohour final exam. Your score on the exam will be tabulated as soon as you complete it. If you do not pass the exam, you may take it again.
Time Commitment: This course should take you a total of 104 hours to complete. Each unit includes a time advisory that lists the amount of time you are expected to spend on each subunit. These should help you plan your time accordingly. It may be useful to take a look at these time advisories to determine how much time you have over the next few weeks to complete each unit and then set goals for yourself. For example, Unit 1 should take you 13 hours. Perhaps you can sit down with your calendar and decide to complete Subunit 1.1 (a total of 3 hours) on Monday night, Subunit 1.2 (a total of 3 hours) on Tuesday night, Subunit 1.3 (a total of 3 hours) on Wednesday night, and so forth.
Tips/Suggestions: The course has been organized so that you will learn the concepts you need for the succeeding unit in the preceding unit. It is essential that you take notes while watching the videos and completing the readings as you progress through the course. In addition, take the homework, practice test, and practice work seriously.
This course has been developed through a partnership with the Washington State Board for Community and Technical Colleges. Unless otherwise noted, all materials are licensed under a Creative Commons Attribution 3.0 Unported License. The Saylor Foundation has modified some materials created by the Washington State Board for Community and Technical Colleges in order to best serve our users.

A version of this course is also available in iTunes U.
Preview the course in your browser or view all our iTunes U courses. 
Learning Outcomes showclose
 simplify and solve linear equations and expressions, including problems with absolute values and applications;
 solve linear inequalities, find equations of lines, and solve application problems;
 add, subtract, multiply, and divide various types of polynomials;
 factor polynomials, and simplify square roots; and
 evaluate, simplify, multiply, divide, add, and subtract rational expressions, and solve basic applications of rational expressions.
Course Requirements showclose
√ have access to a computer;
√ have continuous broadband Internet access;
√ have the ability/permission to install plugins or software (e.g., Adobe Reader or Flash);
√ have the ability to download and save files and documents to a computer;
√ have the ability to open Microsoft files and documents (.doc, .ppt, .xls, etc.);
√ have competency in the English language; and
√ have read the Saylor Student Handbook.
Unit Outline show close
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Unit 1: Review of Major PreAlgebra Concepts
We begin by quickly reviewing the basics of prealgebra concepts. Materials covered in this unit will be familiar to those who have had prealgebra. With a little more practice of the suggested problems and homework, every student, regardless of previous background, should be able to grasp the main concepts.
Unit 1 Time Advisory show close
Unit 1 Learning Outcomes show close

1.1 Review Order of Operations
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 0, Section 0.3: Order of Operations”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 0, Section 0.3: Order of Operations” (PDF)
Instructions: Please read section 0.3 to learn about order of operations. The assignment listed under this subunit corresponds to this reading. Mathematics would be useless if some people thought 3 + 4 x 2 = 14 and others thought 3 + 4 x 2 = 11 . Understanding the order of operations is the most basic (and important) task of the student of mathematics. Note that this reading also covers the material you need to know for subunits 1.1.1–1.1.4.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 0, Section 0.3: Order of Operations”

1.1.1 Removing Parentheses
Note: This subunit is covered by the material beneath subunit 1.1. Notice that the primary rule for order of operations is that things in parentheses be simplified first.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Order of Operations – Introduction”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Order of Operations – Introduction” (PDF)
Instructions: Please complete pages 4 to 6 of Wallace’s workbook to learn about order of operations. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 30 minutes.
Terms of Use: The article above is released under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Order of Operations – Introduction”
Link: YouTube: Tyler Wallace’s “Order of Operations – Introduction” (YouTube)
Instructions: Watch this brief video, which introduces you to the order of operations. Please pay attention to the order in which operations are used and the mnemonic PEMDAS and what it stands for. Note that the video does not make use of the equal sign. Please take a look at The Saylor Foundation’s “Revision to MA001 Video” for a detailed explanation of how to solve the two problems presented in the video.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Order of Operations – Parenthesis”
Link: YouTube: Tyler Wallace’s “Order of Operations – Parenthesis” (YouTube)
Instructions: Watch this brief video. In this video, you will apply PEMDAS to solving problems by first removing parentheses, simplifying exponents, multiplying, dividing, adding, and subtracting. Please understand that regarding multiplication and division, we perform whichever comes first, from left to right.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Order of Operations – Introduction”

1.1.2 Absolute Values
Note: This subunit is covered by the material beneath subunit 1.1. Absolute values tell us how far apart two numbers are, and we need to practice working with absolute value equations.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Order of Operations – Absolute Value”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Order of Operations – Absolute Value” (PDF)
Instructions: Complete pages 7 and 8 of Wallace’s workbook to apply your knowledge about order of operations with absolute values. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Order of Operations – Absolute Value”
Link: YouTube: Tyler Wallace’s “Order of Operations – Absolute Value” (YouTube)
Instructions: Watch this brief, paying attention to the examples being used to explain the concept of absolute values. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Order of Operations – Absolute Value”

1.1.3 The Four Operations on Integers
Note: This subunit is covered by the material beneath subunit 1.1. Notice as you work through the examples that equations with integer coefficients often have solutions that are fractions. Feel free to go back and read or watch the videos if you need to.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Order of Operations – Fractions”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Order of Operations – Fractions” (PDF)
Instructions: Complete page 6 of Wallace’s workbook to practice with the four operations on integers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Order of Operations – Fractions”
Link: YouTube: Tyler Wallace’s “Order of Operations – Fractions” (YouTube)
Instructions: Watch this brief video. Pay attention to the examples being used to explain the concept of four operations on integers. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensedunder a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Order of Operations – Fractions”

1.1.4 Fractions
Note: This subunit is covered by the material beneath subunit 1.1. Fractions allow us to manipulate complicated expressions that include division. Being able to work with fractions allows us to simplify (and often avoid) division.

1.1.5 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Order of Operation”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Order of Operation” (PDF)
Instructions: Review the topics covered in the course so far, and then complete these exercises. Answer only the oddnumbered questions in numbers 1 to 25.
Completing this exercise set should take approximately 1 hour.
Terms of Use: This resource is licensed under Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Order of Operation”

1.2 Simplify Algebraic Expressions
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 0, Section 0.4: Properties of Algebra”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 0, Section 0.4: Properties of Algebra” (PDF)
Instructions: Read this section to learn how to evaluate algebraic expressions for some given values. Note that this reading also covers the material you need to know for subunits 1.2.1–1.2.4.
Reading this section should take approximately 20 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 0, Section 0.4: Properties of Algebra”

1.2.1 Evaluate Expressions
Note: This subunit is covered by the material beneath subunit 1.2. Focus on pages 22 and 23, reading through Example 31.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Simplify Algebraic Expressions – Evaluate”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Simplify Algebraic Expressions – Evaluate” (PDF)
Instructions: Complete page 8 of Wallace’s workbook to evaluate algebraic expressions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Simplify Algebraic Expressions – Evaluate”
Link: YouTube: Tyler Wallace’s “Simplify Algebraic Expressions – Evaluate” (YouTube)
Instructions: Watch this brief video, which discusses how to evaluate expressions. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Simplify Algebraic Expressions – Evaluate”

1.2.2 Combine Like Terms
Note: This subunit is covered by the material beneath subunit 1.2. Focus on page 23.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Simplify Algebraic Expressions – Combine Like Terms”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Simplify Algebraic Expressions – Combine Like Terms” (PDF)
Instructions: Complete page 9 of Wallace’s workbook for practice with combining like terms. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Simplify Algebraic Expressions – Combine Like Terms”
Link: YouTube: Tyler Wallace’s “Simplify Algebraic Expressions – Combine Like Terms” (YouTube)
Instructions: Watch this brief video, paying attention to the examples do the practice problem set on to access your understanding. You may watch the video as often as you please. You may refer to the video when doing your homework if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Simplify Algebraic Expressions – Combine Like Terms”

1.2.3 Distributive Properties
Note: This subunit is covered by the material beneath subunit 1.2. Focus on page 23.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Simplify Algebraic Expressions – Distributive Properties”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Simplify Algebraic Expressions – Distributive Properties” (PDF)
Instructions: Complete page 10 of Wallace’s workbook for practice with simplifying algebraic expressions, using the distributive property. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Simplify Algebraic Expressions – Distributive Property”
Link: YouTube: Tyler Wallace’s “Simplify Algebraic Expressions – Distributive Property” (YouTube)
Instructions: Watch this brief video. Note that when we distribute, we take into consideration the sign of the number we are distributing. Particularly, if you distribute a negative number over a positive number you get a negative number and vice versa. Be careful when you distribute negative numbers.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Simplify Algebraic Expressions – Distributive Properties”

1.2.4 Distribute and Combine Like Terms
Note: This subunit is covered by the material beneath subunit 1.2. Focus on page 24.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Simplify Algebraic Expressions – Distribute and Combine”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Simplify Algebraic Expressions – Distribute and Combine” (PDF)
Instructions: Complete page 11 of Wallace’s workbook for practice with distributing and combining like terms. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Simplify Algebraic Expressions – Distribute and Combine”
Link: YouTube: Tyler Wallace’s “Simplify Algebraic Expressions – Distribute and Combine” (YouTube)
Instructions: Watch this brief video. As we have already familiarized ourselves with distribution in subunit 1.2.3 above, this lesson will expand on that to combine like terms. The goal here is to be able to distribute and combine terms that are alike: terms with the same variable or group of variables and exponents. Remember that combining like terms is simply adding or subtracting the numerical coefficients in the like terms.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Simplify Algebraic Expressions – Distribute and Combine”

1.2.5 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Properties of Algebra”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Properties of Algebra” (PDF)
Instructions: Review the topics covered above, watch the videos, and then do the exercises provided in the link above. Answer every other odd question in 181.
Completing this exercise set should take approximately 2 hours and 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Properties of Algebra”
 1.3 Linear Equations in One Variable

1.3.1 Equality Property of Addition and Multiplication
 Web Media: YouTube: Tyler Wallace’s “Linear Equations – One Step Equations”
Link: YouTube: Tyler Wallace’s “Linear Equations – One Step Equations” (YouTube)
Instructions: Watch this brief video. Note that the takehome message here is that in linear equations, and in other equations you will handle in the future, we can add and multiply same expressions on both sides of the equation. We must do the same thing to each side in order to keep the balance, otherwise we change the solutions to our problem.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Web Media: YouTube: Tyler Wallace’s “Linear Equations – One Step Equations”

1.3.2 Solving One Step Equations
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.1: Solving Linear Equations – One Step Equations”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.1: Solving Linear Equations – One Step Equations” (PDF)
Instructions: Read this section, beginning on page 28, to learn how to solve “one step equations.”
Reading this section should take approximately 10 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: Khan Academy: “Example: Twostep equation with x/4 term”
Link: Khan Academy: “Example: Twostep equation with x/4 term” (Adobe Flash)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. It is attributed to Khan Academy, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Linear Equations – One Step Equations”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Linear Equations – One Step Equations” (PDF)
Instructions: Complete page 12 of Wallace’s workbook for practice with solving one step linear equations.
Completing this worksheet should take approximately 20 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.1: Solving Linear Equations – One Step Equations”

1.3.3 Solving Two Step Equations
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.2: Linear Equations – Two Step Equations”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.2: Linear Equations – Two Step Equations” (PDF)
Instructions: Read section 1.2 on page 33 to learn how to solve “two step equations.” Note that the assignment at the end of this subunit corresponds with this reading.
Reading this section should take approximately 10 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Linear Equations – Two Step Equations”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Linear Equations – Two Step Equations” (PDF)
Instructions: Complete page 13 of Wallace’s workbook for practice with solving two step linear equations. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Linear Equations – Two Step Equations”
Link: YouTube: Tyler Wallace’s “Linear Equations – Two Step Equations” (YouTube)
Instructions: Click on the link above and watch this video to learn how to solve twostep equations. You may watch the video as often as you please. You may refer to the video when doing your homework if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.2: Linear Equations – Two Step Equations”

1.3.4 Solving General Linear Equations in One Variable
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.3: Solving Linear Equations – General Linear Equations”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.3: Solving Linear Equations – General Linear Equations” (PDF)
Instructions: Read this section, beginning on page 37, to learn how to solve general linear equations.
Reading this section should take approximately 10 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Linear Equations – General”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Linear Equations – General” (PDF)
Instructions: Complete page 14 of Wallace’s workbook for practice with simplifying general linear equations with one variable. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions. Note that the video contains a small error in its discussion of Practice B, which will affect the final answer.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Linear Equations – General”
Link: YouTube: Tyler Wallace’s “Linear Equations – General” (YouTube)
Instructions: Watch this brief video, paying attention to the examples being used to explain how to solve general linear equations with one variable. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary. Please note that there is a small math error at the 3:15minute mark in the video; the 5 is not distributed correctly on the right side. The correct answer to the example is 6. For a full explanation of how to solve the problem, please read The Saylor Foundation’s “Revision to Tyler Wallace’s ‘Linear Equations in One Variable’”.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: Khan Academy: “Solving Ax + B = C”
Link: Khan Academy: “Solving Ax + B = C” (Adobe Flash)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. It is attributed to Khan Academy, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.3: Solving Linear Equations – General Linear Equations”

1.3.5 Solving Equations involving Fractions
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.4: Solving Linear Equations – Fractions”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.4: Solving Linear Equations – Fractions” (PDF)
Instructions: Read this section, beginning on page 43, to learn how to solve equations involving fractions.
Reading this section should take approximately 10 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Linear Equations – Fractions” and “Linear Equations – Distributing with Fractions”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Linear Equations – Fractions” and “Linear Equations – Distributing with Fractions” (PDF)
Instructions: Complete pages 15 and 16 of Wallace’s workbook for practice with solving equations with fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing these worksheets should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Linear Equations – Fractions”
Link: YouTube: Tyler Wallace’s “Linear Equations – Fractions” (YouTube)
Instructions: Watch this brief video, which demonstrates how to solve equations that involve fractions. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Linear Equations in One Variable – Distributing with Fractions”
Link: YouTube: Tyler Wallace’s “Linear Equations in One Variable – Distributing with Fractions” (YouTube)
Instructions: Watch this brief video, which explains how to distribute fractions in linear equations that have one variable. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: Khan Academy: “Solving Ax + B = C,” “Identifying Fraction Parts,” and “Equivalent Fractions Example”
Link: Khan Academy: “Solving Ax + B = C” (Adobe Flash), “Identifying Fraction Parts” (Adobe Flash), and “Equivalent Fractions Example” (Adobe Flash)
Instructions: Watch these brief optional videos if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. It is attributed to Khan Academy, and the original version can be found here, here, and here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.4: Solving Linear Equations – Fractions”

1.3.6 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2nd edition: “Practice – Two Step Problems”, “Practice – General Linear Equations”, and “Practice – Fractions”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Two Step Problems” (PDF), “Practice – General Linear Equations” (PDF), and “Practice – Fractions” (PDF)
Instructions: Access the homework assessments. For the first link to section 1.2 of the textbook, answer every other oddnumbered problem in questions 1 through 39. For the second link to section 1.3, complete the oddnumbered problems for questions 1 through 49. For the third link to Ssction 1.4 of the textbook, answer every other oddnumbered problem in questions 1 through 29. Solutions to the problems are given at the end of each PDF.
Completing these exercise sets should take approximately 3 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2nd edition: “Practice – Two Step Problems”, “Practice – General Linear Equations”, and “Practice – Fractions”

1.4 Formulas
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.5: Solving Linear Equations – Formula”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.5: Solving Linear Equations – Formula” (PDF)
Instructions: Read this section. You now have the skills to take a formula that relates two or more quantities and solve it for whichever quantity you want. Notice how this allows us to use formulas in many ways. This is also great practice for algebra skills we will use throughout the course. Note that this reading covers the material you need to know for subunits 1.4.1–1.4.3.
Reading this section should take approximately 20 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.5: Solving Linear Equations – Formula”

1.4.1 Two Step Formulas
Note: This subunit is covered by the material beneath subunit 1.4. Focus on page 47, reading through Example 76.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Formulas – Two Step Formulas”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Formulas – Two Step Formulas” (PDF)
Instructions: Complete page 17 of Wallace’s workbook for practice with twostep formulas. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Formulas – Two Step Formulas”
Link: YouTube: Tyler Wallace’s “Formulas – Two Step Formulas” (YouTube)
Instructions: Watch this brief video, paying attention to the examples being used to explain twostep formulas. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Formulas – Two Step Formulas”

1.4.2 MultiStep Formulas
Note: This subunit is covered by the material beneath subunit 1.4. Focus on page 48.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Formulas – MultiStep Formulas”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Formulas – MultiStep Formulas” (PDF)
Instructions: Complete page 18 of Wallace’s workbook for practice with multistep formulas. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Formulas – MultiStep Formulas”
Link: YouTube: Tyler Wallace’s “Formulas – MultiStep Formulas” (YouTube)
Instructions: Watch this brief video, which explains how to use multistep formulas. Also, note that the four properties you studied earlier in this course are also applicable here. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Formulas – MultiStep Formulas”

1.4.3 Fractions
Note: This subunit is covered by the material beneath subunit 1.4. Focus on page 49.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Formulas – Fractions”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Formulas – Fractions” (PDF)
Instructions: Complete page 19 of Wallace’s workbook for practice with clearing fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Formulas – Fractions”
Link: YouTube: Tyler Wallace’s “Formulas – Fractions” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the examples being used to explain how to clear fractions when using formulas. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Formulas – Fractions”

1.4.4 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Formulas”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Formulas” (PDF)
Instructions: Review the topics, watch the videos, and do the exercises provided in the link above. Answer the oddnumbered questions from 1 to 49. Solutions are given on page 2 of the PDF.
Completing this exercise set should take approximately 1 hour and 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Formulas”

1.5 Absolute Value Equations
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.6: Solving Linear Equations – Absolute Value”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.6: Solving Linear Equations – Absolute Value” (PDF)
Instructions: Read this section. The equations x  3 = 2 and x  3 = 2 are very different from each other, but they are also closely. Notice how we turn an equation with absolute values into two equations without absolute values. Note that this reading covers all the material you need to know for subunits 1.5.1–1.5.3.
Reading this section should take approximately 20 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.6: Solving Linear Equations – Absolute Value”

1.5.1 Two Solutions
Note: This subunit is covered by the material beneath subunit 1.5. Focus on page 52.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Absolute Value – Two Solutions”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Absolute Value – Two Solutions” (PDF)
Instructions: Complete page 20 of Wallace’s workbook to practice solving absolute value equations with two solutions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Absolute Value – Two Solutions”
Link: YouTube: Tyler Wallace’s “Absolute Value – Two Solutions” (YouTube)
Instructions: Watch this fiveminute video, which explains how two solutions are applied to absolute value equations. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Absolute Value – Two Solutions”

1.5.2 Isolate Absolute Value
Note: This subunit is covered by the material beneath subunit 1.5. Focus on pages 52–56.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Absolute Value – Isolate Absolute”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Absolute Value – Isolate Absolute” (PDF)
Instructions: Complete page 21 of Wallace’s workbook for practice with isolating absolute values. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Absolute Value – Isolate Absolute”
Link: YouTube: Tyler Wallace’s “Absolute Value – Isolate Absolute” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the examples being used to explain how to isolate an absolute value. Watch the video as many times as necessary to understand the concept. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Absolute Value – Isolate Absolute”

1.5.3 Two Absolute Values
Note: This subunit is covered by the material beneath subunit 1.5. Focus on page 52.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Absolute Value – Two Absolutes”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Absolute Value – Two Absolutes” (PDF)
Instructions: Complete page 22 of Wallace’s workbook to practice solving for variables with equations that contain two absolute values.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Absolute Value Equations – Two Absolutes”
Link: YouTube: Tyler Wallace’s “Absolute Value Equations – Two Absolutes” (YouTube)
Instructions: Watch this fiveminute video, which demonstrates how to solve absolute value equations when two absolute values are involved. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Absolute Value – Two Absolutes”

1.5.4 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Absolute Value Equations”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Absolute Value Equations” (PDF)
Instructions: Review the topics covered in the course so far, and then complete the exercises linked above. Work on only the oddnumbered questions for numbers 1 through 35. Solutions are given on page 2 of the PDF.
Completing this exercise set should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Absolute Value Equations”

1.6 Introduction to Problem Solving (Word Problems)
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.8: Linear Equations – Number and Geometry”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.8: Linear Equations – Number and Geometry” (PDF)
Instructions: Read this section. Word problems are about gathering information, turning it into equations, and then using the equations to solve the stated problem. Please focus on the various ways that we turn English statements into mathematical equations. Note that this reading covers the material you need to know for subunits 1.6.1–1.6.5.
Reading this section should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.8: Linear Equations – Number and Geometry”

1.6.1 Number Problems
Note: This subunit is covered by the material beneath subunit 1.6. Focus on page 64.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Number Problems”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Number Problems” (PDF)
Instructions: Complete page 23 of Wallace’s workbook to apply your knowledge of consecutive even and odd integers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Word Problems – Number Problems”
Link: YouTube: Tyler Wallace’s “Word Problems – Number Problems” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the examples being used to learn how to translate words into mathematical expressions. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Number Problems”

1.6.2 Consecutive Integers
Note: This subunit is covered by the material beneath subunit 1.6. Focus on pages 70–71.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Consecutive Integers”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Consecutive Integers” (PDF)
Instructions: Complete page 24 of Wallace’s workbook to practice solving word problems with consecutive integers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Word Problems – Consecutive Integers”
Link: YouTube: Tyler Wallace’s “Word Problems – Consecutive Integers” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the examples being used to learn how to solve problems with consecutive integers. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Consecutive Integers”

1.6.3 Consecutive Even/Odd Integers
Note: This subunit is covered by the material beneath subunit 1.6. Focus on the tricks for talking mathematically about even and odd numbers.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Consecutive Even/Odd”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Consecutive Even/Odd” (PDF)
Instructions: Complete page 25 of Wallace’s workbook to apply your knowledge of consecutive even and odd integers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Word Problems – Consecutive Even/Odd”
Link: YouTube: Tyler Wallace’s “Word Problems – Consecutive Even/Odd” (YouTube)
Instructions: Watch this fiveminute video, which shows how to solve problems with consecutive even and odd integers. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Consecutive Even/Odd”

1.6.4 Angles of Triangles
Note: This subunit is covered by the material beneath subunit 1.6. Focus on pages 70 and 71.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Triangles”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Triangles” (PDF)
Instructions: Complete page 26 of Wallace’s workbook to practice solving word problems that involve angles of triangles. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Word Problems – Triangles”
Link: YouTube: Tyler Wallace’s “Word Problems – Triangles” (YouTube)
Instructions: Watch this fiveminute video, which explains how to solve problems using angles of triangles. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Triangles”

1.6.5 Perimeter of Rectangles
Note: This subunit is covered by the material beneath subunit 1.6.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Perimeter”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Perimeter” (PDF)
Instructions: Complete page 27 of Wallace’s workbook to practice solving word problems involving perimeters. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Word Problems – Perimeter”
Link: YouTube: Tyler Wallace’s “Word Problems – Perimeter” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the examples that explain how to problem solve with the perimeter of rectangles. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Word Problems – Perimeter”

1.6.6 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Number and Geometry Problems”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Number and Geometry Problems” (PDF)
Instructions: Review the topics covered so far in this course, and attempt the odd numbered exercises in questions 1 to 45. Solutions are on page 4 of the PDF.
Completing this exercise set should take approximately 1 hour and 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Number and Geometry Problems”
 1.7 Further Application Problems

1.7.1 Variable Age Now
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.9: Solving Linear Equations – Age Problems”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.9: Solving Linear Equations – Age Problems” (PDF)
Instructions: Read this section. Note that this reading also covers the material you need to know for subunit 1.7.2 and correlates to the assignments in subunits 1.7.1 and 1.7.2.
Reading this section should take approximately 10 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Age Problem – Variable Now”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Age Problem – Variable Now” (PDF)
Instructions: Complete page 28 of Wallace’s workbook to practice solving word problems that ask you to solve for a person’s age. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Age Problems – Variable Now”
Link: YouTube: Tyler Wallace’s “Age Problems – Variable Now” (YouTube)
Instructions: Watch this fiveminute video, which demonstrates how to solve age problems. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: Khan Academy: “Age word problems 1” and “Age word problems 2” and “Age word problem 3”
Link: Khan Academy: “Age word problems 1” (Adobe Flash) and “Age word problems 2” (Adobe Flash) and “Age word problem 3” (Adobe Flash)
Instructions: Watch these brief optional videos if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. It is attributed to Khan Academy, and the original version can be found here, here, and here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.9: Solving Linear Equations – Age Problems”

1.7.2 Given Sum Ages Now
Note: This subunit is covered by the material beneath subunit 1.7.1. Note that for all of these problems, we write down two equations from each problem. Translating from the words to the equations can be confusing – especially at first – but we only get good at it through practice.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Age Problem – Sum Now” and “Age Problems – Variable Time”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Age Problem – Sum Now” and “Age Problems – Variable Time” (PDF)
Instructions: Complete pages 29 and 30 of Wallace’s workbook to practice solving word problems to determine ages of a person in the past based on information given about the person’s age now.
Completing these worksheets should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Age Problems – Sum Now”
Link: YouTube: Tyler Wallace’s “Age Problems – Sum Now” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the examples being used to further explain how to solve age problems. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Age Problem – Sum Now” and “Age Problems – Variable Time”

1.7.3 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Age Problems”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Age Problems” (PDF)
Instructions: Answer the odd numbered problems for questions 1 to 39. Solutions are on page 4 of the PDF.
Completing this exercise set should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Age Problems”

Unit 1 Practice Test
 Assessment: Tyler Wallace's Beginning and Intermediate Algebra, 2nd edition: “Unit 1 Practice Test”
Link: Tyler Wallace's Beginning and Intermediate Algebra, 2^{nd} edition: “Unit 1 Practice Test” (PDF)
Instructions: Review Unit 1 before taking this practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. This is very important. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, check your answers against The Saylor Foundation’s “Unit 1 Practice Test – Answer Key”.
Completing this practice test should take approximately 3 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace's Beginning and Intermediate Algebra, 2nd edition: “Unit 1 Practice Test”

Unit 1 Assessment
 Assessment: The Saylor Foundation’s “Unit 1 Assessment”
Link: The Saylor Foundation’s “Unit 1 Assessment” (HTML)
Instructions: Complete this assessment. The correct answers will be displayed when you click Submit. You must be logged into your Saylor Foundation School account in order to access this exam. If you do not yet have an account, you will be able to create one, free of charge, after clicking the link.
 Assessment: The Saylor Foundation’s “Unit 1 Assessment”

Unit 2: Solving Linear Inequalities and Graphing
In this unit, you will learn to apply the concept of solving equations to solve problems involving linear inequalities. You will also learn how to graph a straight line, use different methods to find the slope and intercept of a line, and interpret slope and intercept. You will learn more about types of straight lines.
Unit 2 Time Advisory show close
Unit 2 Learning Outcomes show close

2.1 Inequalities
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 3, Section 3.1: Inequalities – Solve and Graph Inequalities”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 3, Section 3.1: Inequalities – Solve and Graph Inequalities” (PDF)
Instructions: Read this section. Note the difference in meaning among “equal,” “less than,” and “less than or equal,” and the symbols we use for these ideas. Focus on how the steps for solving inequalities are different than for solving equations. Note that this reading covers the material you need to know for subunits 2.1.1–2.1.2.
Reading this section should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 3, Section 3.1: Inequalities – Solve and Graph Inequalities”

2.1.1 Graphing Inequalities
Note: This subunit is covered by the material beneath subunit 2.1. Focus on page 118.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Inequalities – Graphing”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Inequalities – Graphing” (PDF)
Instructions: Complete page 32 of Wallace’s workbook to practice graphing inequalities on a number line. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Inequalities – Graphing”
Link: YouTube: Tyler Wallace’s “Inequalities – Graphing” (YouTube)
Instructions: Watch this fourminute video, paying attention to the examples being used to explain graphing inequalities. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary. In this unit, the operations on the terms are very similar to solving equations. Here, we make use of inequality instead of an equal sign. The inequality sign switches/flips when you multiply or divide both sides by a negative number.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: Khan Academy: “Graphing Inequalities,” “Graphing Linear Inequalities in Two Variables Example 2,” and “Graphing Linear Inequalities in Two Variables Example 3”
Link: Khan Academy: “Graphing Inequalities” (Adobe Flash), “Graphing Linear Inequalities in Two Variables Example 2” (Adobe Flash), and “Graphing Linear Inequalities in Two Variables Example 3” (Adobe Flash)
Instructions: Watch these brief optional videos if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. It is attributed to Khan Academy, and the original version can be found here, here, and here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Inequalities – Graphing”

2.1.2 Interval Notation
Note: This subunit is covered by the material beneath subunit 2.1. We use plots, graphs, and pictures to help us understand and communicate. Interval notation is a very visual way to communicate inequalities, and it also gives us visual techniques for solving them.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Inequalities – Interval Notation”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Inequalities – Interval Notation” (PDF)
Instructions: Complete page 33 of Wallace’s workbook to practice with interval notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Inequalities – Interval Notation”
Link: YouTube: Tyler Wallace’s “Inequalities – Interval Notation” (YouTube)
Instructions: Watch this threeminute video, paying attention to the examples being used to explain interval notation. Note when to use a square bracket and a round bracket. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: Khan Academy: “Absolute Value Inequalities”
Link: Khan Academy: “Absolute Value Inequalities” (Adobe Flash)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. It is attributed to Khan Academy, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Inequalities – Interval Notation”
 2.1.3 Solving Inequalities

2.1.3.1 Solving Linear Inequalities
Note: This subunit is covered by the material beneath subunit 2.1. Focus on pages 118–121.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Inequalities – Solving”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Inequalities – Solving” (PDF)
Instructions: Complete page 34 of Wallace’s workbook to practice solving inequalities. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Inequalities – Solving”
Link: YouTube: Tyler Wallace’s “Inequalities – Solving” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the examples which provide a linear approach to solving inequalities. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Inequalities – Solving”

2.1.3.2 Solve Compound Inequalities (Tripartite)
Note: This subunit is covered by the material beneath subunit 2.1. Focus on page 124.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Inequalities – Tripartite”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Inequalities – Tripartite” (PDF)
Instructions: Complete page 35 of Wallace’s workbook to practice solving inequalities. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Inequalities – Tripartite”
Link: YouTube: Tyler Wallace’s “Inequalities – Tripartite” (YouTube)
Instructions: Watch this fiveminute video. Note that subunit 2.1.3.2 (compound inequalities, or tripartite) is very similar to 2.1.3.1 (solving linear inequalities), except for the way the former has been structured. Bear in mind that in the former, we will be balancing the left center and right. This means whatever you decide to do to the center in order to get the variable in question by itself, you have to do the same to the other two parts of the inequality. Notice also that if you divide or multiply through by a negative number, then you have to flip the inequality signs.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Inequalities – Tripartite”

2.1.4 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Solve and Graph Inequalities” and “Practice – Compound Inequalities”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Solve and Graph Inequalities” (PDF) and “Practice – Compound Inequalities” (PDF)
Instructions: For the first link to section 3.1 of the textbook, answer oddnumbered problems 1 to 37. For the second link to section 3.2 of the textbook, answer all problems, from 1 to 19. Solutions are given at the end of each PDF.
Completing these exercise sets should take approximately 2 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Solve and Graph Inequalities” and “Practice – Compound Inequalities”
 2.2 Graphing, Slopes, and Rate of Change

2.2.1 Point and Lines
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 2, Section 2.1: Graphing – Point and Lines”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 2, Section 2.1: Graphing – Point and Lines” (PDF)
Instructions: Read this section, on pages 89 to 93. One of our most powerful tools is visualization; graphs and XY coordinates comprise the foundation of “seeing” math. Getting comfortable when working with points and lines in a coordinate system is the main point of this section.
Reading these sections should take approximately 20 minuts.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Graphing and Slope – Points and Lines”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Graphing and Slope – Points and Lines” (PDF)
Instructions: Complete page 36 of Wallace’s workbook for practice with graphing based on points provided or equation of the line provided. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Graphing and Slope – Points and Lines”
Link: YouTube: Tyler Wallace’s “Graphing and Slope – Points and Lines” (YouTube)
Instructions: Watch this fiveminute video, which discusses points and lines in graphing and slopes. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: Khan Academy: “Plotting (x,y) relationships”
Link: Khan Academy: “Plotting (x,y) relationships” (Adobe Flash)
Instructions: Watch these brief optional videos if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. It is attributed to Khan Academy, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 2, Section 2.1: Graphing – Point and Lines”

2.2.2 Slope from a Graph
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 2, Section 2.2: Graphing – Slope”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 2, Section 2.2: Graphing – Slope” (PDF)
Instructions: Read this section, which focuses on one fundamental property of the line: its slope. The slope tells us how much the line rises as we move to the right. There are several ways to talk about this one idea. Note that this reading covers the material you need to know for subunit 2.2.3.
Reading this section should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Graphing and Slope – Slope from a Graph”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Graphing and Slope – Slope from a Graph” (PDF)
Instructions: Complete page 37 of Wallace’s workbook to work on determining the slope of a line, given the line on a graph. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Graphing and Slope – Slope from Graph”
Link: YouTube: Tyler Wallace’s “Graphing and Slope – Slope from Graph” (YouTube)
Instructions: Watch this fourminute video, paying attention to the examples being used to explain the slope of a graph. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 2, Section 2.2: Graphing – Slope”

2.2.3 Slope from Two Points
Note: This subunit is covered by the material beneath subunit 2.2.2. Focus on page 96.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Graphing and Slope – Slope from Two Points”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Graphing and Slope – Slope from Two Points” (PDF)
Instructions: Complete page 38 of Wallace’s workbook to work on finding the slope when given two sets of points. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Graphing and Slope – Slope from Two Points”
Link: YouTube: Tyler Wallace’s “Graphing and Slope – Slope from Two Points” (YouTube)
Instructions: Watch this fiveminute video. Take note of the examples used in the video to explain how to find the slope using two points on the graph. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: Khan Academy: “Pointslope and standard form”
Link: Khan Academy: “Pointslope and standard form” (Adobe Flash)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. It is attributed to Khan Academy, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Graphing and Slope – Slope from Two Points”

2.2.4 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Points and Lines” and “Practice – Slope”
Links: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Points and Lines” (PDF) and “Practice – Slope” (PDF)
Instructions: Work through problems 1, 2, and every other odd problem from question 3 through 21 in section 2.1 of the textbook (the first link above). For the second link, please attempt the odd problems from question 1 through 29. Solutions are found at the end of each PDF.
Completing this exercise set should take approximately 2 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Points and Lines” and “Practice – Slope”

2.3 Equations of Lines
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 2, Section 2.3: Graphing – SlopeIntercept Form”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 2, Section 2.3: Graphing – SlopeIntercept Form” (PDF)
Instructions: Read this section. We know what a line is when we see it plotted. There is more than one useful way to write the equation for a line. Note that this reading covers the material you need to know for subunits 2.3.1–2.3.5.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 2, Section 2.3: Graphing – SlopeIntercept Form”

2.3.1 SlopeIntercept Equations
Note: This subunit is covered by the material beneath subunit 2.3. Focus on pages 102 and 103.
 Reading: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Slope Intercept Equation”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Slope Intercept Equation” (PDF)
Instructions: Complete page 39 of Wallace’s workbook to practice providing the slope intercept equation when given information of the slope and yintercept, or a graph. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Equations – Slope Intercept Equation”
Link: YouTube: Tyler Wallace’s “Equations – Slope Intercept Equation” (YouTube)
Instructions: Watch this fiveminute video to learn about the slopeintercept equation and its applications. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: Khan Academy: “Multiple examples of constructing linear equations in slopeintercept form”
Link: Khan Academy: “Multiple examples of constructing linear equations in slopeintercept form” (Adobe Flash)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. It is attributed to Khan Academy, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Slope Intercept Equation”

2.3.2 Putting Equations in Intercept Form
Note: This subunit is covered by the material beneath subunit 2.3. Focus on page 103.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Put in Intercept Form”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Put in Intercept Form” (PDF)
Instructions: Complete page 40 of Wallace’s workbook to practice putting an equation in intercept form. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Equations – Put in Intercept Form”
Link: YouTube: Tyler Wallace’s “Equations – Put in Intercept Form” (YouTube)
Instructions: Watch this fourminute video to learn about putting equations in intercept form. Understand that sometimes there will be no intercept or slope, in which case the slope or intercept will be zero.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Put in Intercept Form”

2.3.3 Equation from Graph
Note: This subunit is covered by the material beneath subunit 2.3. Focus on pages 103 and 104.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Graph”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Graph” (PDF)
Instructions: Complete page 41 of Wallace’s workbook to work on graphing equations. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Reading: YouTube: Tyler Wallace’s “Equations – Graph”
Link: YouTube: Tyler Wallace’s “Equations – Graph” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the examples being used to instruct you on how to graph equations. Be sure that you understand the different parts of the straight line equation and the names that go with them. You may practice by graphing your own lines and seeing if you can label them completely.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Graph”

2.3.4 Vertical and Horizontal Lines
Note: This subunit is covered by the material beneath subunit 2.3. Focus on the end of page 104.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Vertical/Horizontal”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Vertical/Horizontal” (PDF)
Instructions: Complete page 42 of Wallace’s workbook to practice graphing or finding the equations for vertical and horizontal lines. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Equations – Vertical/Horizontal”
Link: YouTube: Tyler Wallace’s “Equations – Vertical/Horizontal” (YouTube)
Instructions: Watch this twominute video, which discusses the different characteristics of vertical and horizontal lines. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Vertical/Horizontal”

2.3.5 PointSlope Equations
Note: This subunit is covered by the material beneath subunit 2.3. Focus on the end of page 104.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Point Slope”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Point Slope” (PDF)
Instructions: Complete page 43 of Wallace’s workbook to practice finding the point slope equation, given a point the line passes through and the slope. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Equations – Point Slope”
Link: YouTube: Tyler Wallace’s “Equations – Point Slope” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the examples being used to demonstrate the pointslope equation.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: Khan Academy: “Pointslope and standard form”
Link: Khan Academy: “Pointslope and standard form” (Adobe Flash)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. It is attributed to Khan Academy, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Point Slope”

2.3.6 Using Two Points to Find the Equation of a Line
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Given Two Points”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Given Two Points” (PDF)
Instructions: Complete page 44 of Wallace’s workbook to practice with finding an equation when given two points. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Equations – Given Two Points”
Link: YouTube: Tyler Wallace’s “Equations – Given Two Points” (YouTube)
Instructions: Watch this fiveminute video, focusing on the examples used to find the equation of the line with two points given.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Equations – Given Two Points”

2.3.7 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – SlopeIntercept” and “Practice – PointSlope Form”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – SlopeIntercept” (PDF) and “Practice – PointSlope Form” (PDF)
Instructions: For the first link to the “Practice – SlopeIntercept,” answer every other oddnumbered problem in questions 1 through 41. For the second link to “Practice – PointSlope Form,” answer every other oddnumbered problem in questions 1 through 51. Solutions appear at the end of each PDF.
Completing these exercise sets should take approximately 3 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – SlopeIntercept” and “Practice – PointSlope Form”

2.4 Parallel and Perpendicular
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 2, Section 2.5: Graphing – Parallel and Perpendicular Lines”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 2, Section 2.5: Graphing – Parallel and Perpendicular Lines” (PDF)
Instructions: Read this section. Parallel lines never intersect, which is good to know if you are looking for an intersection! The shortest distance from a line to something else is perpendicular to the line. The slopes for parallel and perpendicular lines have simple relationships to each other (which you should memorize!). Note that this reading covers the material you need to known for subunits 2.4.1–2.4.2.
Reading this section should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: Khan Academy: “Equations of Parallel and Perpendicular Lines”
Link: Khan Academy: “Equations of Parallel and Perpendicular Lines” (Adobe Flash)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. It is attributed to Khan Academy, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 2, Section 2.5: Graphing – Parallel and Perpendicular Lines”

2.4.1 Slope
Note: This subunit is covered by material beneath subunit 2.4. Of course, we won’t actually understand these ideas without working through problems with parallel and perpendicular lines.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Parallel and Perpendicular – Slope”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Parallel and Perpendicular – Slope” (PDF)
Instructions: Complete page 45 of Wallace’s workbook to practice determining whether lines will be parallel, perpendicular, or neither. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Parallel and Perpendicular – Slope”
Link: YouTube: Tyler Wallace’s “Parallel and Perpendicular – Slope” (YouTube)
Instructions: Watch this fiveminute video, focusing on the examples used to explain how to find the slope of parallel and perpendicular lines. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Parallel and Perpendicular – Slope”

2.4.2 Equations
Note: This subunit is covered by material beneath subunit 2.4 Note that it is all about identifying the slope of a line and finding a point on the line.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Parallel and Perpendicular – Equations”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Parallel and Perpendicular – Equations” (PDF)
Instructions: Complete page 46 of Wallace’s workbook to find the equations of parallel and perpendicular lines. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Parallel and Perpendicular – Equations”
Link: YouTube: Tyler Wallace’s “Parallel and Perpendicular – Equations” (YouTube)
Instructions: Watch this fiveminute video to learn about equations used for parallel and perpendicular lines.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Parallel and Perpendicular – Equations”

2.4.3 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Parallel and Perpendicular Lines”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Parallel and Perpendicular Lines” (PDF)
Instructions: At the link above, answer the oddnumbered problems for questions 1 through 47. Solutions appear on page 3 of the PDF.
Completing this exercise set should take approximately 1 hour and 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Parallel and Perpendicular Lines”

2.5 Distance and Rate Problems
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.10: Solving Linear Equations – Distance, Rate and Time”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.10: Solving Linear Equations – Distance, Rate and Time” (PDF)
Instructions: Read this section. The relationship among distance, rate, and time is one of the simplest and most fundamental of physics and engineering. Notice how d = rt is a relationship that can be solved for any of the three variables. Note that this reading covers the material you need to know for subunits 2.5.1–2.5.3.
Reading this section should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 1, Section 1.10: Solving Linear Equations – Distance, Rate and Time”

2.5.1 Opposite Directions
Note: This subunit is covered by the material beneath subunit 2.5. Focus on page 79.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Distance – Opposite Directions”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Distance – Opposite Directions” (PDF)
Instructions: Complete page 47 of Wallace’s workbook to practice solving distance problems. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Distance – Opposite Directions”
Link: YouTube: Tyler Wallace’s “Distance – Opposite Directions” (YouTube)
Instructions: Watch this fiveminute video, which demonstrates how to solve distance problems involving opposite directions. In working with distance and rate problems, it will be helpful if you begin every question by first drawing a picture and translating the picture into a table as demonstrated in the video. Finally, apply the formula to get the required answer. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Distance – Opposite Directions”

2.5.2 CatchUp
Note: This subunit is covered by the material beneath subunit 2.5. Two objects may be moving in the same direction or in different directions. This is the simplest relationship between two moving objects. “CatchUp” problems are about moving in the same direction but at different speeds.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Distance – Catch Up”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Distance – Catch Up” (PDF)
Instructions: Complete page 48 of Wallace’s workbook to practice solving distance problems. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Distance – Catch Up”
Link: YouTube: Tyler Wallace’s “Distance – Catch Up” (YouTube)
Instructions: Watch this fiveminute video, which demonstrates distance problems in which one person is trying to catch up with another person. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Distance – Catch Up”

2.5.3 Total Time
Note: This subunit is covered by the material beneath subunit 2.5. Focus on pages 79–87.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Distance – Total Time”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Distance – Total Time” (PDF)
Instructions: Complete page 49 of Wallace’s workbook to practice solving distance problems. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Distance – Total Time”
Link: YouTube: Tyler Wallace’s “Distance – Total Time” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the distance and rate problems shown to demonstrate the concept of total time. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Distance – Total Time”

2.5.4 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Distance, Rate, and Time Problems”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Distance, Rate, and Time Problems” (PDF)
Instructions: Answer the oddnumbered problems for questions 1 through 37. Solutions are on page 5 of the PDF.
Completing this exercise set should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Distance, Rate, and Time Problems”

Unit 2 Practice Test
 Assessment: Tyler Wallace's Beginning and Intermediate Algebra, 2nd edition: “Unit 2 Practice Test”
Link: Tyler Wallace's Beginning and Intermediate Algebra, 2^{nd} edition: “Unit 2 Practice Test” (PDF)
Instructions: Review Unit 2 before taking this practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against The Saylor Foundation’s “Unit 2 Practice Test – Answer Key”.
Completing this practice test should take approximately 3 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace's Beginning and Intermediate Algebra, 2nd edition: “Unit 2 Practice Test”

Unit 2 Assessment
 Assessment: The Saylor Foundation’s “Unit 2 Assessment”
Link: The Saylor Foundation’s “Unit 2 Assessment” (HTML)
Instructions: Complete this assessment. The correct answers will be displayed when you click Submit. You must be logged into your Saylor Foundation School account in order to access this exam. If you do not yet have an account, you will be able to create one, free of charge, after clicking the link.
 Assessment: The Saylor Foundation’s “Unit 2 Assessment”

Unit 3: Exponents and Polynomials
This section introduces you to the concept of evaluating exponents, converting scientific notations to decimal notations, and vice versa. You will apply these concepts to evaluating polynomial expressions.
Unit 3 Time Advisory show close
Unit 3 Learning Outcomes show close
 3.1 Exponents

3.1.1 Rules of Exponents
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5: Section 5.1: Polynomials – Exponent Properties”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5: Section 5.1: Polynomials – Exponent Properties” (PDF)
Instructions: Read this section . Polynomials are all about adding and multiplying powers of x. Notice that we have specific rules that govern multiplying and dividing powers of x and raising a power of x to another power. Note that this reading covers the material you need to know for subunits 3.1.1.1–3.1.1.3.
Reading this section should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5: Section 5.1: Polynomials – Exponent Properties”

3.1.1.1 Product Rule
Note: This subunit is covered by the material beneath subunit 3.1.1. Focus on page 177.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Product Rule”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Product Rule” (PDF)
Instructions: Complete page 51 of Wallace’s workbook to practice implementing the product rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Exponents – Product Rule”
Link: YouTube: Tyler Wallace’s “Exponents – Product Rule” (YouTube)
Instructions: Watch this threeminute video, which discusses the product rule for exponents.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Simplify Exponential Expressions – Product and Power Rule”
Link: YouTube: MathIsPower4U’s “Simplify Exponential Expressions – Product and Power Rule” (YouTube)
Instructions: Watch this sixminute video, which discusses the product rule for exponents.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Product Rule”

3.1.1.2 Quotient Rule
Note: This subunit is covered by the material beneath subunit 3.1.1. Focus on page 178.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Quotient Rule”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Quotient Rule” (PDF)
Instructions: Complete page 52 of Wallace’s workbook to practice implementing the quotient rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “ Exponents – Quotient Rule”
Link: YouTube: Tyler Wallace’s “Exponents – Quotient Rule” (YouTube)
Instructions: Watch this threeminute video, which discusses the quotient rule for exponents.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Simplify Exponential Expressions – Quotient Rule”
Link: YouTube: MathIsPower4U’s “Simplify Exponential Expressions – Quotient Rule” (YouTube)
Instructions: Watch this fiveminute video, which discusses the quotient rule for exponents.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Quotient Rule”

3.1.1.3 Power Rule
Note: This subunit is covered by the material beneath subunit 3.1.1. Focus on page 179.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Power Rules”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Power Rules” (PDF)
Instructions: Complete page 53 of Wallace’s workbook to practice implementing the power rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Exponents – Power Rules”
Link: YouTube: Tyler Wallace’s “Exponents – Power Rules” (YouTube)
Instructions: Watch this fiveminute video, which discusses the power rule for exponents.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Simplify Exponential Expressions – Product and Power Rules”
Link: YouTube: MathIsPower4U’s “Simplify Exponential Expressions – Product and Power Rules” (YouTube)
Instructions: Watch this sixminute video, which discusses the power rule for exponents.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Power Rules”

3.1.1.4 Zero Exponents
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.2 Polynomials – Negative Exponents”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.2 Polynomials – Negative Exponents” (PDF)
Instructions: Read this section. Notice that a negative exponent in the denominator is the same as a positive exponent in the numerator. Conversely, a negative exponent in the numerator is the same as a positive exponent in the denominator. Note that this reading covers the material you need to know for subunits 3.1.1.5 and 3.1.2.
Reading this section should take approximately 20 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Zero”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Zero” (PDF)
Instructions: Complete page 54 of Wallace’s workbook to practice with the zero power rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Exponents – Zero”
Link: YouTube: Tyler Wallace’s “Exponents – Zero” (YouTube)
Instructions: Watch this fourminute video, which discusses the zero power rule with exponents. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.2 Polynomials – Negative Exponents”

3.1.1.5 Negative Exponents
Note: This subunit is covered by the material beneath subunit 3.1.1.4. Focus on page 184.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Negative Exponents”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Negative Exponents” (PDF)
Instructions: Complete page 55 of Wallace’s workbook to practice with negative exponents. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Exponents – Negative Exponents”
Link: YouTube: Tyler Wallace’s “Exponents – Negative Exponents” (YouTube)
Instructions: Watch this fiveminute video, which discusses rules for negative exponents.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Simplify Exponential Expressions with Negative Exponents – Basic”
Link: YouTube: MathIsPower4U’s “Simplify Exponential Expressions with Negative Exponents” (YouTube)
Instructions: Watch this fiveminute video, which discusses rules for negative exponents.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.  Web Media: YouTube: El3elmNoor’s “Why X to the Power of Zero Equals One”
Link: YouTube: El3elmNoor’s “Why X to the Power of Zero Equals One” (YouTube)
Instructions: Watch this oneminute video, which shows a short proof of the zero exponent.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Negative Exponents”

3.1.2 Properties
Note: This subunit is covered by the material beneath subunit 3.1.1.4. Focus on page 185.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Properties”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Properties” (PDF)
Instructions: Complete page 56 of Wallace’s workbook to solve equations using the properties of exponents. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Exponents – Properties”
Link: YouTube: Tyler Wallace’s “Exponents – Properties” (YouTube)
Instructions: Watch this fiveminute video, focusing on the examples used that demonstrate how to simplify exponents with the properties and rules you have learned so far, i.e., product rule, quotient rule, etc.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Simplify an Exponential Expression with Negative Exponents”
Link: YouTube: MathIsPower4U’s “Simplify an Exponential Expression with Negative Exponents” (YouTube)
Instructions: Watch this fiveminute video, focusing on the examples used that demonstrate how to simplify exponents with the properties and rules you have learned so far, i.e., product rule, quotient rule, etc.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.  Web Media: YouTube: MathIsPower4U’s “Simplify an Exponential Expression – Positive Exponents Only”
Link: YouTube: MathIsPower4U’s “Simplify an Exponential Expression – Positive Exponents Only” (YouTube)
Instructions: Watch this threeminute video, focusing on the examples used that demonstrate how to simplify exponents with the properties and rules you have learned so far, i.e., product rule, quotient rule, etc.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.  Web Media: YouTube: MathIsPower4U’s “Simplify Expressions with Negative Exponents, Example 4”
Link: YouTube: MathIsPower4U’s “Simplify Expressions with Negative Exponents, Example 4” (YouTube)
Instructions: Watch this threeminute video, focusing on the examples used that demonstrate how to simplify exponents with the properties and rules you have learned so far, i.e., product rule, quotient rule, etc.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Exponents – Properties”

3.1.3 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Exponent Properties” and “Practice – Negative Exponents”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Exponent Properties” (PDF) and “Practice – Negative Exponents” (PDF)
Instructions: For the first link to “Practice – Exponent Properties,” answer the oddnumbered problems for questions 1 through 43. For the second link to “Practice – Negative Exponents,” answer the oddnumbered problems for questions 1 through 39. Solutions appear at the end of each PDF.
Completing these exercise sets should take approximately 3 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Exponent Properties” and “Practice – Negative Exponents”

3.2 Scientific and Decimal Notation
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.3: Polynomials – Scientific Notation”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.3: Polynomials – Scientific Notation” (PDF)
Instructions: Read this section. Scientific notation allows us a general idea of the size of a number with a glance at the exponent, instead of counting places before or after a decimal point. Note that this reading covers the material you need to know for subunits 3.2.1–3.2.4.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.3: Polynomials – Scientific Notation”

3.2.1 Convert
Note: This subunit is covered by the material beneath subunit 3.2. Again, we can’t be confident we understand the idea until we have solved some problems.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Scientific Notation – Convert”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Scientific Notation – Convert” (PDF)
Instructions: Complete page 57 of Wallace’s workbook to practice with converting between standard and scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 20 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Scientific Notation – Convert”
Link: YouTube: Tyler Wallace’s “Scientific Notation – Convert” (YouTube)
Instructions: Watch this fiveminute video, which demonstrates how to convert between standard and scientific notation.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Scientific Notation – Convert”

3.2.2 Close to Scientific
Note: This subunit is covered by the material beneath subunit 3.2. Notice that we use the sign of the exponent to decide whether to count to the left or to the right.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Scientific Notation – Close to Scientific”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Scientific Notation – Close to Scientific” (PDF)
Instructions: Complete page 58 of Wallace’s workbook for more practice with scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Scientific a Notation – Close to Scientific”
Link: YouTube: Tyler Wallace’s “Scientific a Notation – Close to Scientific” (YouTube)
Instructions: Watch this fourminute video, paying attention to the examples being used to further explain scientific notation. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Scientific Notation – Close to Scientific”

3.2.3 Multiply/Divide
Note: This subunit is covered by the material beneath subunit 3.2.1. Focus on page 188.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Scientific Notation – Multiply/Divide”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Scientific Notation – Multiply/Divide” (PDF)
Instructions: Complete page 59 of Wallace’s workbook for more practice with scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Scientific Notation – Multiply/Divide”
Link: YouTube: Tyler Wallace’s “Scientific Notation – Multiply/Divide” (YouTube)
Instructions: Watch this threeminute video, which discusses how to multiply and divide with scientific notation.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Scientific Notation – Multiply/Divide”

3.2.4 Multiply/Divide Leaving Answer in Decimal Notation
Note: This subunit is covered by the material beneath subunit 3.2.1. Focus on page 189.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Scientific Notation – Multiply/Divide where answer is not scientific”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Scientific Notation – Multiply/Divide where answer is not scientific” (PDF)
Instructions: Complete page 60 of Wallace’s workbook to practice with multiplying and dividing scientific notation with a result that is not in scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: The article above is released under a Creative Commons Attribution License 3.0. It is attributed to Tyler Wallace and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Scientific Notation – Multiply/Divide Where Answer Is Not in Scientific Notation”
Link: YouTube: Tyler Wallace’s “Scientific Notation – Multiply/Divide Where Answer Is Not in Scientific Notation” (YouTube)
Instructions: Click on the link above and watch this fourminute video, which addresses multiplication and division and then converting the answer to scientific notation.
Terms of Use: The article above is released under a Creative Commons Attribution License 3.0. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Scientific Notation – Multiply/Divide where answer is not scientific”

3.2.5 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Scientific Notation”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Scientific Notation” (PDF)
Instructions: Answer the oddnumbered problems for questions 1 through 41. Solutions appear on page 2 of the PDF.
Completing this exercise set should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution License 3.0. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Scientific Notation”
 3.3 Polynomials

3.3.1 Evaluate
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.4: Polynomials – Introduction to Polynomials”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.4: Polynomials – Introduction to Polynomials” (PDF)
Instructions: Read this section. Evaluating a polynomial is simply plugging in a value for the variable and then simplifying. Note that this reading covers the material you need to know for subunit 3.3.2.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Polynomials – Evaluate”
Link: YouTube: Tyler Wallace’s “Polynomials – Evaluate” (YouTube)
Instructions: Watch this fiveminute video, which provides definitions and characteristics of polynomials and gives examples of evaluating polynomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.4: Polynomials – Introduction to Polynomials”

3.3.2 Add/Subtract
Note: This subunit is covered by the material beneath subunit 3.3.1. Focus on page 193.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Add/Subtract”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Add/Subtract” (PDF)
Instructions: Complete page 62 of Wallace’s workbook to practice adding and subtracting polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Polynomials – Add and Subtract”
Link: YouTube: Tyler Wallace’s “Polynomials – Add and Subtract” (YouTube)
Instructions: Watch this fourminute video, paying attention to the examples being used to add and subtract polynomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Add/Subtract”
 3.3.3 Multiply Polynomials

3.3.3.1 Monomial by Polynomial
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.5: Polynomials – Multiplying Polynomials”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.5: Polynomials – Multiplying Polynomials” (PDF)
Instructions: Read this section. Multiplying polynomials is all about being careful with distribution (focus on how parentheses are used to make sure we distribute correctly) and following the rules for exponents (focus on how we use x^{p} x^{q} = x^{p+q}). Note that this reading covers the material you need to know for subunits 3.3.3.2–3.3.3.4.
Reading this section should take approximately 20 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Multiply by Monomials”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Multiply by Monomials” (PDF)
Instructions: Complete page 63 of Wallace’s workbook to practice multiplying by monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Polynomials – Multiply by Monomial”
Link: YouTube: Tyler Wallace’s “Polynomials – Multiply by Monomial” (YouTube)
Instructions: Watch this threeminute video, paying attention to the examples being used to explain how to multiply by monomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.5: Polynomials – Multiplying Polynomials”

3.3.3.2 Binomial by Binomial (FOIL)
Note: This subunit is covered by the material beneath subunit 3.3.3.1. Focus on page 197.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Multiply by Binomials”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Multiply by Binomials” (PDF)
Instructions: Complete page 64 of Wallace’s workbook to practice multiplying by binomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Polynomials – Multiply by Binomials”
Link: YouTube: Tyler Wallace’s “Polynomials – Multiply by Binomials” (YouTube)
Instructions: Watch this fourminute video, paying attention to the explain of how to multiply binomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution License 3.0. It is attributed to Tyler Wallace and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Multiply by Binomials”

3.3.3.3 Multiply with Trinomials
Note: This subunit is covered by the material beneath subunit 3.3.3.1. It is vital to get practice with these multiplications because we will later need to be able to go backwards!
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Multiply by Trinomials”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Multiply by Trinomials” (PDF)
Instructions: Complete page 65 of Wallace’s workbook to practice multiplying by trinomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Polynomials – Multiply by Trinomials”
Link: YouTube: Tyler Wallace’s “Polynomials – Multiply by Trinomials” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the explaination of how to multiply trinomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Multiply by Trinomials”

3.3.3.4 Multiply Monomial by Two Binomials
Note: This subunit is covered by the material beneath subunit 3.3.3.1. Try to be patient; these problems take a while, but they are great practice.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Multiply Monomials and Binomials”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Multiply Monomials and Binomials” (PDF)
Instructions: Complete page 66 of Wallace’s workbook to practice multiplying monomials by binomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Polynomials – Multiply Monomial by Binomials”
Link: YouTube: Tyler Wallace’s “Polynomials – Multiply Monomial by Binomials” (YouTube)
Instructions: Watch this fourminute video, paying attention to the examples being used to explain how to multiply monomials by two binomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution License 3.0. It is attributed to Tyler Wallace and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Multiply Monomials and Binomials”
 3.3.4 Special Products

3.3.4.1 Sums and Difference
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.6: Polynomials – Multiply Special Products”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.6: Polynomials – Multiply Special Products” (PDF)
Instructions: Read this section. The idea of this section is to point out a few nice and important special cases of polynomial multiplication. Memorize these special products and it will pay off big later! Note that this reading also covers the material you need to know for subunit 3.3.4.2.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Sums and Difference”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Sums and Difference” (PDF)
Instructions: Complete page 67 of Wallace’s workbook to practice multiplying monomials by binomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Polynomials – Sum and Difference”
Link: YouTube: Tyler Wallace’s “Polynomials – Sum and Difference” (YouTube)
Instructions: Watch this threeminute video, paying attention to the examples being used to explain sums and differences with polynomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Simplify an Expression Involving Squares of Binomials”
Link: YouTube: MathIsPower4U’s “Simplify an Expression Involving Squares of Binomials” (YouTube)
Instructions: Watch this threeminute video, paying attention to the examples being used to explain sums and differences with polynomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.  Web Media: TheLearningPub’s “Factoring Polynomials – Difference of Two Squares”
Link: YouTube: TheLearningPub’s “Factoring Polynomials – Difference of two Squares” (YouTube)
Instructions: Watch this threeminute video, paying attention to the examples being used to explain sums and differences with polynomials.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.6: Polynomials – Multiply Special Products”

3.3.4.2 Perfect Square
Note: This subunit is covered by the reading assigned beneath subunit 3.3.4.1. Here we are introducing you to some very useful facts that we turn into great tricks later.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Perfect Square”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Perfect Square” (PDF)
Instructions: Complete page 68 of Wallace’s workbook to practice with perfect squares. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Polynomials – Perfect Square”
Link: YouTube: Tyler Wallace’s “Polynomials – Perfect Square” (YouTube)
Instructions: Watch this fourminute video, which discusses the perfect square shortcut.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Factoring a Perfect Square Trinomial”
Link: YouTube: MathIsPower4U’s “Factoring a Perfect Square Trinomial” (YouTube)
Instructions: Watch this eightminute video, which discusses the perfect square shortcut.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Polynomials – Perfect Square”

3.3.5 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Introduction to Polynomials,” “Practice – Multiply Polynomials,” and “Practice – Multiply Special Products”
Links: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Introduction to Polynomials” (PDF), “Practice – Multiply Polynomials” (PDF), and “Practice – Multiply Special Products” (PDF)
Instructions: For the first link to “Practice – Introduction to Polynomials,” answer every other odd numbered problem for questions 1 through 41. For the second link to “Practice – Multiply Polynomials,” answer odd numbered problems for questions 1 through 39. For the third link to “Practice – Multiply Special Products,” answer odd numbered problems for questions 1 through 39. Solutions appear at the end of each PDF.
Completing these exercise sets should take approximately 4 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Introduction to Polynomials,” “Practice – Multiply Polynomials,” and “Practice – Multiply Special Products”
 3.4 Division of Polynomials

3.4.1 Divide a Polynomial by Monomial – Part I
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.7: Polynomials – Divide Polynomials”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.7: Polynomials – Divide Polynomials” (PDF)
Instructions: Read this section. Dividing polynomials is just the same as the long division you learned in elementary school. It is also great practice in solidifying your skills in exponents and multiplication. Pay special attention to how the exponents work as place holders just as the digits in the 1s, 10s, 100s, and so forth, places did for us in elementary school. Note that this reading covers the material you need to know for subunits 3.4.2 and 3.4.3.
Reading this section should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Division – By Monomials”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Division – By Monomials” (PDF)
Instructions: Complete page 69 of Wallace’s workbook to practice dividing monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Division – By Monomials part 1”
Link: YouTube: Tyler Wallace’s “Division – By Monomials part 1” (YouTube)
Instructions: Watch this fourminute video, which discusses division by monomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 5, Section 5.7: Polynomials – Divide Polynomials”

3.4.2 Divide a Polynomial by Monomial – Part 2
Note: This subunit is covered by the material beneath subunit 3.4.1. Focus on page 206.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Division – By Polynomials”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Division – By Polynomials” (PDF)
Instructions: Complete page 70 of Wallace’s workbook to practice dividing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Division – By Monomials part 2”
Link: YouTube: Tyler Wallace’s “Division – By Monomials part 2” (YouTube)
Instructions: Watch this fiveminute video, which continues to discuss dividing by monomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Division – By Polynomials”

3.4.3 Divide a Polynomial by a Polynomial
Note: This subunit is covered by the material beneath subunit 3.4.1. Focus on page 206.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Division – Missing Terms”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Division – Missing Terms” (PDF)
Instructions: Complete page 71 of Wallace’s workbook for more practice with dividing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Division – Polynomials”
Link: YouTube: Tyler Wallace’s “Division – Polynomials” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the examples being used to explain the division of polynomials. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Divide a Polynomial by a Binomial using Long Division”
Link: YouTube: MathIsPower4U’s “Divide a Polynomial by a Binomial using Long Division” (YouTube)
Instructions: Watch this fiveminute video, which continues to discuss dividing by monomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Division – Missing Terms”

3.4.4 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Divide Polynomials”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Divide Polynomials” (PDF)
Instructions: Answer oddnumbered problems for questions 1 through 43. Keep in mind that you are allowed to watch the videos as often as you please to help you answer the homework problems. Solutions appear at the end of the PDF.
Completing this exercise set should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Divide Polynomials”

Unit 3 Practice Test
 Assessment: Tyler Wallace's Beginning and Intermediate Algebra, 2nd edition: “Unit 3 Practice Test”
Link: Tyler Wallace's Beginning and Intermediate Algebra, 2^{nd} edition: “Unit 3 Practice Test” (PDF)
Instructions: Review Unit 3 before clicking on the link above to take the practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against the Saylor Foundation’s “Unit 3 Practice Test – Answer Key”. [Disagree with an answer? View and discuss errata here.]
Completing this practice test should take approximately 3 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace's Beginning and Intermediate Algebra, 2nd edition: “Unit 3 Practice Test”

Unit 3 Assessment
 Assessment: The Saylor Foundation’s “Unit 3 Assessment”
Link: The Saylor Foundation’s “Unit 3 Assessment” (HTML)
Instructions: Complete this assessment. The correct answers will be displayed when you click Submit. You must be logged into your Saylor Foundation School account in order to access this exam. If you do not yet have an account, you will be able to create one, free of charge, after clicking the link.
 Assessment: The Saylor Foundation’s “Unit 3 Assessment”

Unit 4: Factoring Polynomials
This unit expands on what you learned in Unit 3. In Unit 4, you will learn to factor the greatest common factor by grouping and other factoring methods. Because factoring and distribution are opposite actions, you will be able to determine whether you have factored correctly by going in the opposite direction, which is distributing through multiplication.
Unit 4 Time Advisory show close
Unit 4 Learning Outcomes show close

4.1 Greatest Common Factor (GCF) and Grouping
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.1: Factoring – Greatest Common Factor”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.1: Factoring – Greatest Common Factor” (PDF)
Instructions: Read this section. Pay special attention to page 212. Note that this reading also covers the material you need to know for subunits 4.1.1 and 4.1.2.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.1: Factoring – Greatest Common Factor”

4.1.1 Find the GCF
Note: This subunit is covered by the material beneath subunit 4.1. Finding the GCF takes practice. Please don’t be discouraged if you don’t find the GCF at first: we can always factor more later!
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “GCF and Grouping – Find the GCF”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “GCF and Grouping – Find the GCF” (PDF)
Instructions: Complete page 73 of Wallace’s workbook to practice finding the greatest common factor. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “GCF and Grouping – Find GCF”
Link: YouTube: Tyler Wallace’s “GCF and Grouping – Find GCF” (YouTube)
Instructions: Watch this twominute video, which discusses how to find the Greatest Common Factor (GCF). You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “GCF and Grouping – Find the GCF”

4.1.2 Factor the GCF
Note: This subunit is covered by the material beneath subunit 4.1. Notice how we are doing the reverse of multiplying polynomials. These factoring problems are both challenging and necessary, so don’t go on without being able to do these problems.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “GCF and Grouping – Factor GCF”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “GCF and Grouping – Factor GCF” (PDF)
Instructions: Complete page 74 of Wallace’s workbook to practice factoring the greatest common factor. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “GCF and Grouping – Factor GCF”
Link: YouTube: Tyler Wallace’s “GCF and Grouping – Factor GCF” (YouTube)
Instructions: Watch this fourminute video to learn how to factor the Greatest Common Factor (GCF).
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Factor and Solve a Polynomial Equation”
Link: YouTube: MathIsPower4U’s “Factor and Solve a Polynomial Equation” (YouTube)
Instructions: Watch this fiveminute video to learn how to factor the Greatest Common Factor (GCF).
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “GCF and Grouping – Factor GCF”

4.1.3 Grouping
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.2: Factoring – Grouping”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.2: Factoring – Grouping” (PDF)
Instructions: Read this section. Pay special attention to page 216. Note that this reading also covers the material you need to know for subunit 4.1.4.
Reading this section should take approximately 20 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “GCF and Grouping – Binomial GCF”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “GCF and Grouping – Binomial GCF” (PDF)
Instructions: Complete page 75 of Wallace’s workbook to practice factoring the greatest common factor. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “GCF and Grouping – Grouping”
Link: YouTube: Tyler Wallace’s “GCF and Grouping – Grouping” (YouTube)
Instructions: Watch this fourminute video, which discusses the GCF and grouping methods. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: SharonOfTheRose’s “Factoring a Monomial from a Polynomial and Factor by Grouping”
Link: YouTube: SharonOfTheRose’s “Factoring a Monomial from a Polynomial and Factor by Grouping” (YouTube)
Instructions: Watch this thirteenminute video to learn how to factor the Greatest Common Factor (GCF).
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.2: Factoring – Grouping”

4.1.4 Grouping with Order Change
Note: This subunit is covered by the material beneath subunit 4.1.3. You may take different steps than in the video – or even more steps – but please make sure that: (1) you get the same result and (2) that you understand the steps taken in the video.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “GCF and Grouping – Grouping” and “GCF and Grouping – Change Order”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “GCF and Grouping – Grouping” (PDF) and “GCF and Grouping – Change Order” (PDF)
Instructions: Complete pages 76 and 77 of Wallace’s workbook to practice with grouping and order change. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing these worksheets should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “GCF and Grouping – Change Order”
Link: YouTube: Tyler Wallace’s “GCF and Grouping – Change Order” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the examples being used to explain grouping with order change. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “GCF and Grouping – Grouping” and “GCF and Grouping – Change Order”

4.1.5 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Greatest Common Factor” and “Practice – Grouping”
Links: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Greatest Common Factor” (PDF) and “Practice – Grouping” (PDF)
Instructions: For the first link to “Practice – Greatest Common Factor,” answer every other oddnumbered problem for questions 1 through 31. For the second link to “Practice – Grouping,” answer oddnumbered problems for questions 1 through 27. Solutions appear at the end of each PDF.
Completing these exercise sets should take approximately 2 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Greatest Common Factor” and “Practice – Grouping”

4.2 Factoring Trinomials
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.3: Factoring – Trinomials Where a = 1”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.3: Factoring – Trinomials Where a = 1” (PDF)
Instructions: Read this section. Pay special attention to page 221. Note that this reading covers the material you need to know for subunits 4.2.1 and 4.2.2.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.3: Factoring – Trinomials Where a = 1”

4.2.1 Leading Coefficient Is 1 – Part 1
Note: This subunit is covered by the material beneath subunit 4.2. This method of factoring (the ac method) really is the workhorse of factoring trinomials: We need two numbers whose product is the constant term and whose sum is the x coefficient.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Trinomials – a = 1”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Trinomials – a = 1” (PDF)
Instructions: Complete page 80 of Wallace’s workbook to practice with trinomials when a = 1. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Trinomials – a = 1”
Link: YouTube: Tyler Wallace’s “Trinomials – a = 1” (YouTube)
Instructions: Watch this threeminute video, paying attention to the examples being used to explain how to factor trinomials when a is equal to 1. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Factor Trinomials when A equals 1”
Link: YouTube: MathIsPower4U’s “Factor Trinomials when A equals 1” (YouTube)
Instructions: Watch this fiveminute video. Pay attention to the examples being used to explain how to factor trinomials when a is equal to 1. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Trinomials – a = 1”

4.2.2 Leading Coefficient Is 1 with GCF – Part 2
Note: This subunit is covered by the material beneath subunit 4.2. The idea here is to first factor out the GCF, leaving a much simpler problem to factor.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Trinomials – a = 1 with GCF”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Trinomials – a = 1 with GCF” (PDF)
Instructions: Complete page 81 of Wallace’s workbook for more practice with trinomials when a = 1. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Trinomials – a = 1 with GCF”
Link: YouTube: Tyler Wallace’s “Trinomials – a = 1 with GCF” (YouTube)
Instructions: Watch this fourminute video for a continuation of the video that explains how to factor trinomials when a is equal to 1.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Trinomials – a = 1 with GCF”

4.2.3 Leading Coefficient Is Not 1 – Part 1
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.4: Factoring – Trinomials Where a ≠ 1”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.4: Factoring – Trinomials Where a ≠ 1” (PDF)
Instructions: Read this section. When we multiply polynomials we are distributing across parentheses. Here we are doing the reverse: We are trying to write a polynomial as a product of factors. We will introduce several techniques, and you should focus on learning them all because later it will be up to you to match the correct technique to a given problem. Note that this reading also covers the material you need to know for subunits 4.2.4 and 4.2.5.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Trinomials – a ≠ 1”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Trinomials – a ≠ 1” (PDF)
Instructions: Complete page 78 of Wallace’s workbook for practice with trinomials when a ≠ 1. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Trinomials – a ≠ 1 Part 1”
Link: YouTube: Tyler Wallace’s “Trinomials – a ≠ 1 Part 1” (YouTube)
Instructions: Watch this fourminute video. Pay attention to the examples used to describe how to factor trinomials when the leading coefficient is not 1. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.4: Factoring – Trinomials Where a ≠ 1”

4.2.4 Leading Coefficient Is Not 1 – Part 2
Note: This subunit is covered by the material beneath subunit 4.2.3. Focus on page 226.
 Web Media: YouTube: Tyler Wallace’s “Trinomials – a ≠ 1 Part 2”
Link: YouTube: Tyler Wallace’s “Trinomials – a ≠ 1 Part 2” (YouTube)
Instructions: Watch this fourminute video, which continues to demonstrate how trinomials can be factored when the leading coefficient is not 1.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Factor Trinomials when A is NOT equal to 1 – Grouping Method”
Link: YouTube: MathIsPower4U’s “Factor Trinomials when A is NOT equal to 1 – Grouping Method” (YouTube)
Instructions: Watch this fourminute video, which continues to demonstrate how trinomials can be factored when the leading coefficient is not 1.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Web Media: YouTube: Tyler Wallace’s “Trinomials – a ≠ 1 Part 2”

4.2.5 Leading Coefficient Is Not 1 with GCF – Part 1
Note: This subunit is covered by the material beneath subunit 4.2.3. Focus on page 227.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Trinomials – a ≠ 1 with GCF”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Trinomials – a ≠ 1 with GCF” (PDF)
Instructions: Complete page 79 of Wallace’s workbook for more practice with trinomials when a ≠ 1. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Trinomials – a ≠ 1 with GCF Part 1”
Link: YouTube: Tyler Wallace’s “Trinomials – a ≠ 1 with GCF Part 1” (YouTube)
Instructions: Watch this fourminute video, paying attention to the examples being used to explain the concept in this unit.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Trinomials – a ≠ 1 with GCF”

4.2.6 Leading Coefficient Is Not 1 with GCF – Part 2
 Web Media: YouTube: Tyler Wallace’s “Trinomials – a ≠ 1 with GCF Part 2”
Link: YouTube: Tyler Wallace’s “Trinomials – a ≠ 1 with GCF Part 2” (YouTube)
Instructions: Watch this fourminute video. Pay attention to the examples being used to explain the concept in this unit. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Web Media: YouTube: Tyler Wallace’s “Trinomials – a ≠ 1 with GCF Part 2”

4.2.7 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Trinomials Where a = 1” and “Practice – Trinomials Where a ≠ 1”
Links: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Trinomials Where a = 1” (PDF) and “Practice – Trinomials Where a ≠ 1” (PDF)
Instructions: For the first link to “Practice – Trinomials Where a = 1,” answer the oddnumbered problems 1to 25. For the second link to “Practice – Trinomials Where a ≠ 1,” answer the oddnumbered problems 1 to 39. Solutions appear at the end of each PDF.
Completing these exercise sets should take approximately 2 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Trinomials Where a = 1” and “Practice – Trinomials Where a ≠ 1”

4.3 Special Products
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.5: Factoring – Factoring Special Products”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.5: Factoring – Factoring Special Products” (PDF)
Instructions: Read this section. There is an error in Exercise 308 on page 231. You can find the correction in the Saylor Foundation’s “Correction to Exercise 308, Page 231”. Note that this reading covers the material you need to know for subunits 4.3.1–4.3.6.
Reading this section should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.5: Factoring – Factoring Special Products”

4.3.1 Difference of Squares
Note: This subunit is covered by the material beneath subunit 4.3. Oh, when you notice the difference of squares, you’re happy! The more that you practice, the more likely you are to notice!
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Difference of Squares”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Difference of Squares” (PDF)
Instructions: Complete page 82 of Wallace’s workbook to reinforce your understanding of differences of squares. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Special Products – Difference of Squares”
Link: YouTube: Tyler Wallace’s “Special Products – Difference of Squares” (YouTube)
Instructions: Watch this threeminute video, which discusses the difference of squares.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Factoring a Difference of Squares”
Link: YouTube: MathIsPower4U’s “Factoring a Difference of Squares” (YouTube)
Instructions: Watch this fiveminute video, which discusses the difference of squares.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Difference of Squares”

4.3.2 Sum of Squares
Note: This subunit is covered by the material beneath subunit 4.3. Focus on page 230.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Sum of Squares”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Sum of Squares” (PDF)
Instructions: Complete page 83 of Wallace’s workbook to reinforce your understanding of sum of squares. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Special Products – Sum of Squares”
Link: YouTube: Tyler Wallace’s “Special Products – Sum of Squares” (YouTube)
Instructions: Watch this twominute video, which discusses the sum of squares. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Sum of Squares”

4.3.3 Difference of 4^{th} Powers
Note: This subunit is covered by the material beneath subunit 4.3. Focus on page 231.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Difference of 4^{th} Powers”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Difference of 4^{th} Powers” (PDF)
Instructions: Complete page 84 of Wallace’s workbook to reinforce your understanding the difference of 4^{th} powers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: Tyler Wallace’s “Special Products – Difference of 4^{th} Powers”
Link: Tyler Wallace’s “Special Products – Difference of 4^{th} Powers” (YouTube)
Instructions: Watch this fourminute video, which addresses how to use fourth powers. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Difference of 4^{th} Powers”

4.3.4 Perfect Square
Note: This subunit is covered by the material beneath subunit 4.3. Focus on page 232.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Perfect Squares”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Perfect Squares” (PDF)
Instructions: Complete page 85 of Wallace’s workbook for practice with perfect squares. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Special Products – Perfect Square”
Link: YouTube: Tyler Wallace’s “Special Products – Perfect Square” (YouTube)
Instructions: Watch this fourminute video, which discusses perfect squares.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Factoring a Perfect Square Trinomial”
Link: YouTube: MathIsPower4U’s “Factoring a Perfect Square Trinomial” (YouTube)
Instructions: Watch this eightminute video, which discusses perfect square trinomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Perfect Squares”

4.3.5 Cubes
Note: This subunit is covered by the material beneath subunit 4.3. Focus on pages 231 and 232. Note that there is an error in Exercise 308 on page 231. You can find a correction in The Saylor Foundation’s “Correction to Exercise 308, Page 231”.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Cubes”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Cubes” (PDF)
Instructions: Complete page 86 of Wallace’s workbook to practice with cubes. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Special Products – Cubes”
Link: YouTube: Tyler Wallace’s “Special Products – Cubes” (YouTube)
Instructions: Watch this fiveminute video, paying attention to the examples being used to explain the concept of cubes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Factoring a Sum or Difference of Cubes”
Link: YouTube: MathIsPower4U’s “Factoring a Sum or Difference of Cubes” (YouTube)
Instructions: Watch this sixminute video. Pay attention to the examples being used to explain the concept of cubes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – Cubes”

4.3.6 GCF
Note: This subunit is covered by the material beneath subunit 4.3. Focus on page 233.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – GCF”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – GCF” (PDF)
Instructions: Complete page 87 of Wallace’s workbook for practice with the greatest common factor in terms of special products. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Special Products – GCF”
Link: YouTube: Tyler Wallace’s “Special Products – GCF” (YouTube)
Instructions: Watch this threeminute video, paying attention to the examples being used to explain the concept of special products with the GCF. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Special Products – GCF”

4.3.7 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Factoring Special Products”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Factoring Special Products” (PDF)
Instructions: Answer all of the oddnumbered problems for questions 1 through 47. Solutions appear on page 2 of the PDF.
Completing this exercise set should take approximately 1 hour and 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Factoring Special Products”
 4.4 Factoring Strategy

4.4.1 Strategy
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.6: Factoring – Factoring Strategy”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.6: Factoring – Factoring Strategy” (PDF)
Instructions: Read this section. Pay special attention to page 234. Note that this reading corresponds to the workbook assignment at the end of this subunit.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Factoring Strategy – Strategy”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Factoring Strategy – Strategy” (PDF)
Instructions: Complete page 88 of Wallace’s workbook to reinforce your knowledge of when to use certain methods of factoring. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Factoring Strategy”
Link: YouTube: Tyler Wallace’s “Factoring Strategy” (YouTube)
Instructions: Watch this fiveminute video, which discusses factoring strategies. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: YouTube: Bigbend Emporium's “Factoring Strategy”
Link: YouTube: Bigbend Emporium's “Factoring Strategy” (YouTube)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Bigbed Emporium.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.6: Factoring – Factoring Strategy”

4.4.2 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.7: Factoring – Solve by Factoring”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.7: Factoring – Solve by Factoring” (PDF)
Instructions: Read this section. Here we emphasize how we can solve problems by factoring. Focus on the rule – “if ab = 0, then a = 0 or b = 0 (or both)” – and how factoring makes this rule so important. Note that this reading covers the material you need to know for subunits 4.5.1–4.5.4.
Reading this section should take approximately 20 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.7: Factoring – Solve by Factoring”

4.5 Solve by Factoring
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.7: Factoring – Solve by Factoring”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.7: Factoring – Solve by Factoring” (PDF)
Instructions: Read this section. Here we emphasize how we can solve problems by factoring. Focus on the rule – “if ab = 0, then a = 0 or b = 0 (or both)” – and how factoring makes this rule so important. Note that this reading covers the material you need to know for subunits 4.5.1–4.5.4.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 6, Section 6.7: Factoring – Solve by Factoring”

4.5.1 Zero Product Property
Note: This subunit is covered by the material beneath subunit 4.5. Here we put the ab = 0 rule into practice.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Solve by Factoring – Zero Product Property”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Solve by Factoring – Zero Product Property” (PDF)
Instructions: Complete page 89 of Wallace’s workbook to reinforce your knowledge of the zero product property. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Solve by Factoring – Zero Product Rule”
Link: YouTube: Tyler Wallace’s “Solve by Factoring – Zero Product Rule” (YouTube)
Instructions: Watch this fourminute video. Pay attention to the examples being used to explain the zero product rule.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “The ZeroProduct Property”
Link: YouTube: MathIsPower4U’s “The ZeroProduct Property” (YouTube)
Instructions: Watch this sixminute video. Pay attention to the examples being used to explain the zero product rule.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.  Optional Web Media: YouTube: MathIsPower4U’s “Solve an Equation in Factored Form”
Link: YouTube: MathIsPower4U’s “Solve an Equation in Factored Form” (YouTube)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Solve by Factoring – Zero Product Property”

4.5.2 Need to Factor
Note: This subunit is covered by the material beneath subunit 4.5. Focus on page 238.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Solve by Factoring – Need to Factor”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Solve by Factoring – Need to Factor” (PDF)
Instructions: Complete page 90 of Wallace’s workbook for practice with factoring. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Solve by Factoring – Need to Factor”
Link: YouTube: Tyler Wallace’s “Solve by Factoring – Need to Factor” (YouTube)
Instructions: Watch this fourminute video. Pay attention to the examples to demonstrate how to solve by factoring.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: YouTube: MathIsPower4U’s “Solve Quadratic Equations by Factoring Completely”
Link: YouTube: MathIsPower4U’s “Solve Quadratic Equations by Factoring Completely” (YouTube)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic. Several videos follow which demonstrate how to solve variations on this kind of problem. These are also optional.
Factor and Solve Quadratic Equation – Greatest Common Factor Only
Factor and Solve Quadratic Equation – Difference of Squares
Factor and Solve Quadratic Equation – Trinomial a = 1, Ex. 1
Factor and Solve Quadratic Equation – Trinomial a = 1, Ex. 2
Factor and Solve Quadratic Equation – Trinomial a = 1
Factor and Solve Quadratic Equation – Perfect Square Trinomials
Factor and Solve Quadratic Equation – a ≠ 1, Ex. 1
Factor and Solve Quadratic Equation – a ≠ 1, Ex. 2
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Solve by Factoring – Need to Factor”

4.5.3 Make Equal to Zero
Note: This subunit is covered by the material beneath subunit 4.5. Focus on page 239.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Solve by Factoring – Equal to Zero”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Solve by Factoring – Equal to Zero” (PDF)
Instructions: Complete page 91 of Wallace’s workbook for practice with factoring. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Solve by Factoring – Make Equal to Zero”
Link: YouTube: Tyler Wallace’s “Solve by Factoring – Make Equal to Zero” (YouTube)
Instructions: Watch this fiveminute video. Pay attention to the examples being used to explain how to factor by making the equation equal zero.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Solve by Factoring – Equal to Zero”

4.5.4 Simplifying Needed
Note: This subunit is covered by the material beneath subunit 4.5. Focus on page 240.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Solve by Factoring – Simplify”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Solve by Factoring – Simplify” (PDF)
Instructions: Complete page 92 of Wallace’s workbook for practice with simplifying and factoring. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Solve by Factoring – Simplify First”
Link: YouTube: Tyler Wallace’s “Solve by Factoring – Simplify First” (YouTube)
Instructions: Watch this fiveminute video, focusing on the examples that discuss how to simplify equations. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Solve by Factoring – Simplify”

4.5.5 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Solve by Factoring”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Solve by Factoring” (PDF)
Instructions: Answer all of the oddnumbered problems for questions 1 through 35. Solutions appear on page 2 of the PDF.
Completing this exercise set should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Solve by Factoring”

Unit 4 Practice Test
 Assessment: Tyler Wallace's Beginning and Intermediate Algebra, 2nd edition: “Unit 4 Practice Test”
Link: Tyler Wallace's Beginning and Intermediate Algebra, 2^{nd} edition: “Unit 4 Practice Test” (PDF)
Instructions: Review Unit 4 before taking this practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against the Saylor Foundation’s “Unit 4 Practice Test – Answer Key”.
Completing this practice test should take approximately 3 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace's Beginning and Intermediate Algebra, 2nd edition: “Unit 4 Practice Test”

Unit 4 Assessment
 Assessment: The Saylor Foundation’s “Unit 4 Assessment”
Link: The Saylor Foundation’s “Unit 4 Assessment” (HTML)
Instructions: Complete this assessment. The correct answers will be displayed when you click Submit. You must be logged into your Saylor Foundation School account in order to access this exam. If you do not yet have an account, you will be able to create one, free of charge, after clicking the link.
 Assessment: The Saylor Foundation’s “Unit 4 Assessment”

Unit 5: Rational Expression
In this unit, you will learn how to evaluate rational expressions and perform operations such as addition, multiplication, and division involving rational expressions. You will apply the concept of multiplying rational expressions to dimensional analysis, where you will convert units from single/dual unit of measurement to another.
Unit 5 Time Advisory show close
Unit 5 Learning Outcomes show close

5.1 Reduce Rational Expressions
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.1 Rational Expressions – Reduce Rational Expressions”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.1 Rational Expressions – Reduce Rational Expressions” (PDF)
Instructions: Read this section. Rational expressions are just fractions and fractions of polynomials. Focus on the use of the rules of exponentiation and when we can cancel in fractions. Note that this reading will cover the material you need to know for subunits 5.1.1–5.1.4.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.1 Rational Expressions – Reduce Rational Expressions”

5.1.1 Evaluate
Note: This subunit is covered by the material beneath subunit 5.1. Focus on page 243.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Reduce – Evaluate”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Reduce – Evaluate” (PDF)
Instructions: Complete page 94 of Wallace’s workbook for practice with reducing rational expressions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Reduce – Evaluate”
Link: YouTube: Tyler Wallace’s “Reduce – Evaluate” (YouTube)
Instructions: Watch this fourminute video. Pay attention to the examples being used to explain evaluate rational expressions.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Reduce – Evaluate”

5.1.2 Reduce Fractions
Note: This subunit is covered by the material beneath subunit 5.1. Focus on page 244.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Reduce – Reduce Fractions”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Reduce – Reduce Fractions” (PDF)
Instructions: Complete page 95 of Wallace’s workbook for practice with reducing fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Reduce – Reduce Fractions”
Link: YouTube: Tyler Wallace’s “Reduce – Reduce Fractions” (YouTube)
Instructions: Watch this twominute video. Pay attention to the examples being used to explain the concept of reducing fractions in rational expressions. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Reduce – Reduce Fractions”

5.1.3 Reduce Monomials
Note: This subunit is covered by the material beneath subunit 5.1. Focus on page 245.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Reduce – Monomials”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Reduce – Monomials” (PDF)
Instructions: Complete page 96 of Wallace’s workbook for practice with reducing monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Reduce – Monomials”
Link: YouTube: Tyler Wallace’s “Reduce – Monomials” (YouTube)
Instructions: Watch this threeminute video. Pay attention to the examples being used to explain the concept in this unit.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: YouTube: MathIsPower4U’s “Simplifying Rational Expressions – Monomials”
Link: YouTube: MathIsPower4U’s “Simplifying Rational Expressions – Monomials” (YouTube)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Reduce – Monomials”

5.1.4 Reduce Polynomials
Note: This subunit is covered by the material beneath subunit 5.1. Focus on page 246.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Reduce – Polynomials”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Reduce – Polynomials” (PDF)
Instructions: Complete page 97 of Wallace’s workbook for practice with reducing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “ Reduce – Polynomials”
Link: YouTube: Tyler Wallace’s “Reduce – Polynomials” (YouTube)
Instructions: Watch this fiveminute video which discusses how to reduce polynomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: YouTube: MathIsPower4U’s “Ex 2: Simplify Rational Expressions,” “Ex 3: Simplify Rational Expressions,” and “Ex 4: Simplify Rational Expressions”
Link: YouTube: MathIsPower4U’s “Ex 2: Simplify Rational Expressions” (YouTube), “Ex 3: Simplify Rational Expressions” (YouTube), and “Ex 4: Simplify Rational Expressions” (YouTube)
Instructions: Watch these brief optional videos if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Reduce – Polynomials”

5.1.5 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Reduce Rational Expressions”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Reduce Rational Expressions” (PDF)
Instructions: Answer all of the oddnumbered problems for questions 1 through 49. Solutions appear on page 3 of the PDF.
Completing this exercise set should take approximately 1 hour and 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Reduce Rational Expressions”

5.2 Multiply & Divide Rational Expressions
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.2: Rational Expression – Multiply & Divide”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.2: Rational Expression – Multiply & Divide” (PDF)
Instructions: Read this section. Again, rules for exponents are paramount, but now focus on dividing as “inverting and multiplying.” Note this reading covers the material you need to know for subunits 5.2.1–5.2.4.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.2: Rational Expression – Multiply & Divide”

5.2.1 Multiply & Divide Fractions
Note: This subunit is covered by the material beneath subunit 5.2. Focus on page 248.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Multiply and Divide – Fractions”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Multiply and Divide – Fractions” (PDF)
Instructions: Complete page 98 of Wallace’s workbook for practice with multiplying and dividing fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Multiply and Divide – Fractions”
Link: YouTube: Tyler Wallace’s “Multiply and Divide – Fractions” (YouTube)
Instructions: Watch this fourminute video. Pay attention to the examples being used to show how to multiply and divide fractions.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: YouTube: MathIsPower4U’s “Multiplication Involving Fractions,” “Multiplying Signed Fractions,” “Multiplying Three Fractions,” and “Multiplying Three Signed Fractions”
Link: YouTube: MathIsPower4U’s “Multiplication Involving Fractions” (YouTube), “Multiplying Signed Fractions” (YouTube), “Multiplying Three Fractions” (YouTube), and “Multiplying Three Signed Fractions” (YouTube)
Instructions: Watch these brief optional videos if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Multiply and Divide – Fractions”

5.2.2 Multiply & Divide Monomials
Note: This subunit is covered by the material beneath subunit 5.2. Focus on page 249.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Multiply and Divide – Monomials”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Multiply and Divide – Monomials” (PDF)
Instructions: Complete page 99 of Wallace’s workbook for practice with multiplying and dividing monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Multiply and Divide – Monomials”
Link: YouTube: Tyler Wallace’s “Multiply and Divide – Monomials” (YouTube)
Instructions: Watch this fiveminute video which discusses the multiplication and division of monomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: MathIsPower4U’s “Multiply Rational Expressions – Monomials” and “Dividing Rational Expressions – Monomials”
Link: YouTube: MathIsPower4U’s “Multiply Rational Expressions – Monomials” (YouTube) and “Dividing Rational Expressions – Monomials” (YouTube)
Instructions: Watch these optional videos if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Multiply and Divide – Monomials”

5.2.3 Multiply & DIvide Polynomials
Note: This subunit is covered by the material beneath subunit 5.2. Focus on pages 250 and 251.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Multiply and Divide – Polynomials”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Multiply and Divide – Polynomials” (PDF)
Instructions: Complete page 100 of Wallace’s workbook for practice with multiplying and dividing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Multiply and Divide – Polynomials”
Link: YouTube: Tyler Wallace’s “Multiply and Divide – Polynomials” (YouTube)
Instructions: Watch this fiveminute video which discusses the multiplication and division of polynomials. Remember that you may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Multiply and Divide – Both at Once”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Multiply and Divide – Both at Once” (PDF)
Instructions: Complete page 101 of Wallace’s workbook for practice with multiplying and dividing polynomials both at once. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 20 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Multiply and Divide – Both at Once Part 1”
YouTube: Tyler Wallace’s “Multiply and Divide – Both at Once Part 1” (YouTube)
Instructions: Watch this fiveminute video. Pay attention to the examples being used that involve both multiplication and division at once.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: Tyler Wallace’s Multiply and Divide – “Both at Once Part 2”
Link: Tyler Wallace’s “Multiply and Divide – Both at Once Part 2” (YouTube)
Instructions: Watch this fiveminute video, which discusses examples that involve both multiplication and division at once.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: YouTube: MathIsPower4U’s “Ex 2: Multiply Rational Expressions”
Link: YouTube: MathIsPower4U’s “Ex 2: Multiply Rational Expressions” (YouTube)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic. Several videos follow which demonstrate how to solve variations on this kind of problem. These are also optional.
Ex 3: Multiply Rational Expressions
Ex 4: Multiply Rational Expressions
Ex 2: Dividing Rational Expressions
Ex 3: Dividing Rational Expressions
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Multiply and Divide – Polynomials”

5.2.4 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Multiply and Divide”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Multiply and Divide” (PDF)
Instructions: Answer all of the oddnumbered problems for questions 1 through 43. Solutions appear on page 3 of the PDF.
Completing this exercise set should take approximately 1 hour and 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Multiply and Divide”

5.3 Least Common Denominator (LCD)
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.3: Rational Expressions – Least Common Denominators”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.3: Rational Expressions – Least Common Denominators” (PDF)
Instructions: Read this section. One of the skills students have most difficulty with is adding fractions. You can make this much easier by understanding least common denominators. Note that this reading covers the material you need to know for subunits 5.3.1–5.3.3.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.3: Rational Expressions – Least Common Denominators”

5.3.1 Numbers
Note: This subunit is covered by the material beneath subunit 5.3. Focus on page 253.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “LCD – Numbers”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “LCD – Numbers” (PDF)
Instructions: Complete page 102 of Wallace’s workbook for practice with the Lowest Common Denominator (LCD). Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “LCD – Numbers”
Link: YouTube: Tyler Wallace’s “LCD – Numbers” (YouTube)
Instructions: Watch this fiveminute video, which discusses the Least Common Denominator (LCD). You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: YouTube: MathIsPower4U’s “Determining the Least Common Multiple Using a List of Multiples” and “Determining the Least Common Multiple Using Prime Factorization”
Link: YouTube: MathIsPower4U’s “Determining the Least Common Multiple Using a List of Multiples” (YouTube) and “Determining the Least Common Multiple Using Prime Factorization” (YouTube)
Instructions: Watch these brief optional videos if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “LCD – Numbers”

5.3.2 Monomials
Note: This subunit is covered by the material beneath subunit 5.3. Focus on page 254.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “LCD – Monomials”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “LCD – Monomials” (PDF)
Instructions: Complete page 103 of Wallace’s workbook for more practice with Lowest Common Denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “LCD – Monomials”
Link: YouTube: Tyler Wallace’s “LCD – Monomials” (YouTube)
Instructions: Watch this threeminute video which discusses the Least Common Denominator with monomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: YouTube: Bigbend Emporium's “Least Common Multiple (LCM) with Variables”
YouTube: Bigbend Emporium's “Least Common Multiple (LCM) with Variables” (YouTube)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Bigbend Emporium.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “LCD – Monomials”

5.3.3 Polynomials
Note: This subunit is covered by the material beneath subunit 5.3. Focus on page 255.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “LCD – Polynomials”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “LCD – Polynomials” (PDF)
Instructions: Complete page 104 of Wallace’s workbook for more practice with Lowest Common Denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “LCD – Polynomials”
Link: YouTube: Tyler Wallace’s “LCD – Polynomials” (YouTube)
Instructions: Watch this fiveminute video which discusses the Least Common Denominator with polynomials.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “LCD – Polynomials”

5.3.4 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Least Common Denominator”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Least Common Denominator” (PDF)
Instructions: Answer questions 11–20. If necessary, use the videos and information in this subunit to help you solve these problems. Solutions appear on page 2 of the PDF.
Completing this exercise set should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Least Common Denominator”

5.4 Add & Subtract Rational Expressions
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.4: Rational Expressions – Add & Subtract”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.4: Rational Expressions – Add & Subtract” (PDF)
Instructions: Read this section and complete the corresponding workbook assignment for this subunit. Notice that most of the work involves finding a common denominator; once that is done, we simply need to be careful with multiplication. Note that this reading covers the material you need to know for subunits 5.4.1 and 5.4.2.1.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.4: Rational Expressions – Add & Subtract”

5.4.1 Add & Subtract Fractions
Note: This subunit is covered by the material beneath subunit 5.4. If you need to watch the video below to do these problems, you may do so. Then after you watch it, come back and work through them.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Add and Subtract – Fractions”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Add and Subtract – Fractions” (PDF)
Instructions: Complete page 105 of Wallace’s workbook for practice with adding and subtracting fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Add and Subtract – Common Denominator”
Link: YouTube: Tyler Wallace’s “Add and Subtract – Common Denominator” (YouTube)
Instructions: Watch this fiveminute video. Pay attention to the examples being used to explain how to add and subtract fractions.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: YouTube: MathIsPower4U’s “Adding Fractions with Different Denominators”
Link: YouTube: MathIsPower4U’s “Adding Fractions with Different Denominators” (YouTube)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic. Several videos follow which demonstrate how to solve variations on this kind of problem. These are also optional.
Adding Fractions with Unlike Denominators
Adding Signed Fractions, Ex 1
Adding Signed Fractions, Ex 2
Subtract Fractions with Unlike Denominators
Subtracting Signed Fractions, Ex 1
Subtracting Signed Fractions, Ex 2
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Add and Subtract – Fractions”
 5.4.2 Add & Subtract Rational Expressions with Different Denominators

5.4.2.1 Different Denominator – Part 1
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.5: Add and Subtract Rational Expressions: Different Denominator (Part 1)”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.5: Add and Subtract Rational Expressions: Different Denominator (Part 1)” (PDF)
Instructions: Read this section and complete the corresponding workbook assignment for the subunit. Note that this reading covers the material you need to know for subunit 5.4.2.3.
Reading this section should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Add and Subtract – Common Denominator”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Add and Subtract – Common Denominator” (PDF)
Instructions: Complete page 106 of Wallace’s workbook for practice with adding and subtracting common denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Add and Subtract – Different Denominators (part 1)”
Link: YouTube: Tyler Wallace’s “Add and Subtract – Different Denominators Part 1” (YouTube)
Instructions: Watch this fiveminute video. Pay attention to the examples used to explain adding and subtracting when there are different denominators. Here, one would first obtain a common denominator for the expressions involved and then proceed as in subunit 5.4.2.1 above.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: YouTube: MathIsPower4U’s “Ex 1: Add and Subtract Rational Expressions  Like Denominators,” “Ex 2: Add and Subtract Rational Expressions  Like Denominators,” and “Ex 3: Add and Subtract Rational Expressions  Like Denominators”
Link: YouTube: MathIsPower4U’s “Ex 1: Add and Subtract Rational Expressions  Like Denominators” (YouTube), “Ex 2: Add and Subtract Rational Expressions  Like Denominators” (YouTube), and “Ex 3: Add and Subtract Rational Expressions  Like Denominators” (YouTube)
Instructions: Watch these brief optional videos if you feel like you need additional help with this topic.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.5: Add and Subtract Rational Expressions: Different Denominator (Part 1)”

5.4.2.2 Different Denominator – Part 2
Note: This subunit is covered by the material beneath subunit 5.4.2.2. These are great problems; you need to factor and then find a common denominator before adding. If you aren’t able to finish a problem, come back and do it after watching the video below.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Add and Subtract – Different Denominators”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Add and Subtract – Different Denominators” (PDF)
Instructions: Complete page 107 of Wallace’s workbook for practice with adding and subtracting different denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Add and Subtract – Different Denominators Part 2”
Link: YouTube: Tyler Wallace’s “Add and Subtract – Different Denominators Part 2” (YouTube)
Instructions: Watch this fiveminute video which discusses adding and subtracting when there are different denominators. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Optional Web Media: YouTube: MathIsPower4U’s “Add and Subtract Rational Expressions  Opposite Denominators”
Link: YouTube: MathIsPower4U’s “Add and Subtract Rational Expressions  Opposite Denominators” (YouTube)
Instructions: Watch this brief optional video if you feel like you need additional help with this topic. Several videos follow which demonstrate how to solve variations on this kind of problem. These are also optional.
Ex 1: Add and Subtract Rational Expressions  Unlike Denominators
Ex 2: Add and Subtract Rational Expressions  Unlike Denominators
Ex 3: Add and Subtract Rational Expressions  Unlike Denominators
Ex 4: Add and Subtract Rational Expressions  Unlike Denominators
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to James L. Sousa.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Add and Subtract – Different Denominators”

5.4.3 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Add and Subtract”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Add and Subtract” (PDF)
Instructions: Answer the oddnumbered problems for questions 1 through 43. Solutions appear on page 2 of the PDF.
Completing this exercise set should take approximately 1 hour and 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Add and Subtract”

5.5 Dimensional Analysis
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.8: Rational Expressions – Dimensional Analysis”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.8: Rational Expressions – Dimensional Analysis” (PDF)
Instructions: Read this section and complete the corresponding workbook assignment for this subunit. Notice how converting from minutes to hours or feet to miles or cups to gallons all have the same foolproof method: canceling units of measurement. Note that this reading covers the material you need to know for subunits 5.5.1–5.5.2.
This reading should take approximately 45 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Reading: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Chapter 7, Section 7.8: Rational Expressions – Dimensional Analysis”

5.5.1 Convert Single Unit
Note: This subunit is covered by the material beneath subunit 5.5. Focus on page 279.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Dimensional Analysis – Convert Single Unit”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Dimensional Analysis – Convert Single Unit” (PDF)
Instructions: Complete page 108 of Wallace’s workbook for practice with dimensional analysis in which you convert single units. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Reading: YouTube: Tyler Wallace’s “Dimensional Analysis – Convert Single Unit”
Link: YouTube: Tyler Wallace’s “Dimensional Analysis – Convert Single Unit” (YouTube)
Instructions: Watch this fiveminute video which discusses converting single units. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Dimensional Analysis – Convert Single Unit”

5.5.2 Convert Dual Unit
Note: This subunit is covered by the material beneath subunit 5.5. Focus on page 280.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Dimensional Analysis – Convert Two Units”
Link: Tyler Wallace’s Beginning Algebra Lab Notebook: “Dimensional Analysis – Convert Two Units” (PDF)
Instructions: Complete page 109 of Wallace’s workbook for practice with dimensional analysis with converting dual units. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
Completing this worksheet should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.  Web Media: YouTube: Tyler Wallace’s “Dimensional Analysis – Convert Two Units”
Link: YouTube: Tyler Wallace’s “Dimensional Analysis – Convert Two Units” (PDF)
Instructions: Watch this fiveminute video which discusses converting dual units.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Activity: Tyler Wallace’s Beginning Algebra Lab Notebook: “Dimensional Analysis – Convert Two Units”

5.5.3 Homework Assessment
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Dimensional Analysis”
Link: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Dimensional Analysis” (PDF)
Instructions: Answer all of the problems. Solutions appear on page 3 of the PDF.
Completing this assessment should take approximately 2 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace’s Beginning and Intermediate Algebra, 2^{nd} edition: “Practice – Dimensional Analysis”

Unit 5 Practice Test
 Assessment: Tyler Wallace's Beginning and Intermediate Algebra, 2nd edition: “Unit 5 Practice Test”
Link: Tyler Wallace's Beginning and Intermediate Algebra, 2^{nd} edition: “Unit 5 Practice Test” (PDF)
Instructions: Review Unit 5 before taking this practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against the Saylor Foundation’s “Unit 5 Practice Test – Answer Key”.
Completing this practice test should take about 3 hours.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Tyler Wallace, and the original version can be found here.
 Assessment: Tyler Wallace's Beginning and Intermediate Algebra, 2nd edition: “Unit 5 Practice Test”

Unit 5 Assessment
 Assessment: The Saylor Foundation’s “Unit 5 Assessment”
Link: The Saylor Foundation’s “Unit 5 Assessment” (HTML)
Instructions: Complete this assessment. The correct answers will be displayed when you click Submit. You must be logged into your Saylor Foundation School account in order to access this exam. If you do not yet have an account, you will be able to create one, free of charge, after clicking the link.
 Assessment: The Saylor Foundation’s “Unit 5 Assessment”

Final Exam
 Final Exam: The Saylor Foundation’s “MA001 Final Exam”
Link: The Saylor Foundation’s “MA001 Final Exam” (HTML)
Instructions: You must be logged into your Saylor Foundation School account in order to access this exam. If you do not yet have an account, you will be able to create one, free of charge, after clicking the link.
 Final Exam: The Saylor Foundation’s “MA001 Final Exam”

NCCRS Credit Recommended Exam
 Reading: The Saylor Foundation's "MA001 Final Exam"
Link: The Saylor Foundation's "MA001 Final Exam" (HTML)
Instructions: The above linked exam has been specially created as part of our National College Credit Recommendation Service (NCCRS) review program. Successfully passing this exam will make students eligible to receive a transcript with 3 hours of recommended college credit.
Please note that because this exam has the possibility to be a creditbearing exam, it must be administered in a proctored environment, and is therefore password protected. Further information about Saylor's NCCRS program and the options and requirements for proctoring, can be found here. Please make sure to read this page carefully before attempting this exam.
If you choose to take this exam, you may want to first take the regular, certificatebearing MA001 Final Exam as a practice test, which you can find above.
 Reading: The Saylor Foundation's "MA001 Final Exam"