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.
Completing this unit should take you approximately 19 hours.
Upon successful completion of this unit, you will be able to:
- remove a common factor;
- factor by grouping (including rearranging terms);
- factor special products;
- factor trinomials; and
- solve quadratic equations by factoring.
4.1: Greatest Common Factor (GCF) and Grouping
Read this section. Pay special attention to page 212.
4.1.1: Find the GCF
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.
Watch this two-minute 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.
4.1.2: Factor the GCF
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.
Watch these videos to learn how to factor the Greatest Common Factor (GCF).
4.1.3: Grouping
Read this section. Pay special attention to page 216.
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.
Watch these videos, which discuss the GCF and grouping methods. You may watch the videos as often as you please. You may refer to the videos when doing your homework, if necessary.
4.1.4: Grouping with Order Change
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.
Watch this five-minute 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.
You may take different steps than in the video - or even more steps - but please make sure that you get the same result and that you understand the steps taken in the video.
4.1.5: Homework Assessment
Answer every other odd-numbered problem for questions 1 through 31.
Answer every other odd-numbered problem for questions 1 through 27.
4.2: Factoring Trinomials
Read this section. Pay special attention to page 221.
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.
4.2.1: Leading Coefficient Is 1 - Part 1
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.
Watch these videos, paying attention to the examples used to explain how to factor trinomials when a is equal to 1. You may watch the videos as often as you please. You may refer to the video when doing your homework, if necessary.
4.2.2: Leading Coefficient Is 1 with GCF - Part 2
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.
Watch this four-minute video for a continuation of the video that explains how to factor trinomials when a is equal to 1.
4.2.3: Leading Coefficient Is Not 1 - Part 1
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.
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.
Watch this four-minute 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.
4.2.4: Leading Coefficient Is Not 1 - Part 2
- Watch these videos, which demonstrate how trinomials can be factored when the leading coefficient is not 1.
4.2.5: Leading Coefficient Is Not 1 with GCF - Part 1
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.
Watch this four-minute video, paying attention to the examples being used to explain the concept in this unit.
4.2.6: Leading Coefficient Is Not 1 with GCF - Part 2
Watch this four-minute 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.
4.2.7: Homework Assessment
Answer the odd-numbered problems 1 to 25.
Answer the odd-numbered problems 1 to 39.
4.3: Special Products
Read this section. There is an error in Exercise 308 on page 231. You can find the correction in Saylor Academy's "Correction to Exercise 308, Page 231".
4.3.1: Difference of Squares
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.
Watch these videos, which discuss the difference of squares.
4.3.2: Sum of Squares
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.
Watch this two-minute 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.
4.3.3: Difference of 4th Powers
Complete page 84 of Wallace's workbook to reinforce your understanding the difference of 4th 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.
Watch this four-minute 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.
4.3.4: Perfect Square
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.
Watch these videos, which discuss perfect squares and perfect square trinomials.
4.3.5: Cubes
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.
Watch these videos, which explain the concept of cubes.
4.3.6: GCF
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.
Watch this three-minute 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.
4.3.7: Homework Assessment
Answer all of the odd-numbered problems for questions 1 through 47.
4.4: Factoring Strategy
4.4.1: Strategy
Read this section. Pay special attention to page 234. Note that this reading corresponds to the workbook assignment at the end of this subunit.
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.
Watch these videos, which discuss factoring strategies. You may watch the videos as often as you please. You may refer to the videos when doing your homework, if necessary.
4.4.2: Homework Assessment
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.
4.5: Solve by Factoring
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.
4.5.1: Zero Product Property
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.
Watch these videos, which explain the zero product rule.
4.5.2: Need to Factor
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.
Watch this four-minute video. Pay attention to the examples to demonstrate how to solve by factoring.
4.5.3: Make Equal to Zero
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.
Watch this five-minute video. Pay attention to the examples being used to explain how to factor by making the equation equal zero.
4.5.4: Simplifying Needed
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.
Watch this five-minute 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.
4.5.5: Homework Assessment
Answer all of the odd-numbered problems for questions 1 through 35.
Unit 4 Practice Test
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 "Unit 4 Practice Test - Answer Key".
Unit 4 Assessment
- Receive a grade
Take this assessment to see how well you understood this unit.
- This assessment does not count towards your grade. It is just for practice!
- You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
- You can take this assessment as many times as you want, whenever you want.
