# Chapter 7: Polynomials

**Advanced**Created by: CK-12

## Introduction

Here you'll learn all about polynomials. You'll start by learning how to add, subtract, and multiply polynomials. Then you will learn how to factor polynomials, which can be thought of as the opposite of multiplying. Next you'll learn how to divide polynomials and how this connects to factoring. Finally, you'll learn how to use your graphing calculator to graph polynomials in order to determine the factors and roots of polynomials.

## Chapter Outline

- 7.1. Addition and Subtraction of Polynomials
- 7.2. Multiplication of Polynomials
- 7.3. Special Products of Polynomials
- 7.4. Monomial Factors of Polynomials
- 7.5. Factorization of Quadratic Expressions
- 7.6. Special Cases of Quadratic Factorization
- 7.7. Zero Product Property for Quadratic Equations
- 7.8. Applications of Quadratic Equations
- 7.9. Complete Factorization of Polynomials
- 7.10. Factorization by Grouping
- 7.11. Factorization of Special Cubics
- 7.12. Division of a Polynomial by a Monomial
- 7.13. Long Division and Synthetic Division
- 7.14. The Factor Theorem
- 7.15. Graphs of Polynomial Functions

### Chapter Summary

## Summary

You learned that adding, subtracting, and multiplying polynomials all rely on the distributive property. You also learned that factoring is the reverse of multiplying because when you factor a polynomial you are trying to rewrite the polynomial as a product of other polynomials. You learned how to factor completely by first looking for common factors and then using other methods to factor the remaining expression. You learned special cases of factoring to watch out for including the difference of perfect squares, perfect square trinomials, and the sum and difference of cubes. You learned how factoring can allow you to solve a quadratic equation with the help of the zero product property.

You learned how to divide polynomials and how dividing polynomials can connect to factoring. You learned about the factor theorem and that polynomial long division can actually help you to factor higher degree polynomials. Finally, you learned that factors of polynomials connect to their x-intercepts, and that you can use a graphing calculator to graph polynomial functions in order to find out more information about the factors of the polynomial.