# Chapter 12: Polynomials

## Introduction

Here you will learn about polynomials. In the beginning, you will learn how to identify monomials, binomials, trinomials and polynomials. You will understand how to write them in standard form and how to classify them according to degree. Simplifying polynomials, evaluating polynomial expressions and adding and subtracting polynomials comes next. After that, you will learn to multiply monomials including how to apply different properties to operations with monomials. Next, you will learn how to identify a parabola. You will learn how to multiply binomials by using FOIL. Next, you will see how quadratic equations connect to parabolas and will work with quadratic equations, tables and graphs. Then you will learn about quadratic functions and their graphs. Then, you will learn about exponential functions including exponential growth and decay. The concluding Concepts of the chapter will focus on arithmetic and geometric sequences.

## Chapter Outline

- 12.1. Recognize and Identify Monomials, Binomials and Trinomials
- 12.2. Write and Classify Polynomials in Standard Form
- 12.3. Simplify Polynomials by Combining Like Terms
- 12.4. Evaluate Polynomial Expressions
- 12.5. Adding Polynomials
- 12.6. Subtracting Polynomials
- 12.7. Multiplying Monomials
- 12.8. Recognize and Apply the Power of a Product Property
- 12.9. Recognize and Apply the Power of a Quotient Property
- 12.10. Recognize and Apply the Power of a Power Property
- 12.11. Multiplying Binomials
- 12.12. Understanding the Graphs of a Parabola
- 12.13. Understanding the Equations of Parabolas
- 12.14. Recognizing Quadratic Functions
- 12.15. Evaluating Quadratic Functions
- 12.16. Exponential Functions
- 12.17. Exponential Growth and Decay
- 12.18. Arithmetic Sequences
- 12.19. Geometric Sequences

### Chapter Summary

## Summary

You began this chapter by learning about polynomials. In the beginning, you learned how to identify monomials, binomials, trinomials and polynomials. You wrote them in standard form and classified them according to degree. Simplifying polynomials, evaluating polynomial expressions and adding and subtracting polynomials came next. After that, you learned to multiply monomials, and applied properties to multiplying monomials. This helped you to learn different rules. You also learned to multiply binomials by using FOIL.

Next, you identified parabolas, their graphs and equations. You learned how quadratic equations connect to parabolas and completed tasks involving quadratic equations, tables and graphs. Then you learned about quadratic functions and their graphs.

Finally,you explored exponential functions including exponential growth and decay. Then you learned the difference between arithmetic sequences and geometric sequences. You learned how to identify these sequences, find differences in patterns and identify common ratios. This concluded your work in this chapter.