# Ch 16: High School Algebra: Properties of Polynomial Functions

### About This Chapter

## Properties of Polynomial Functions - Chapter Summary and Learning Objectives

In these lessons our instructors will show you how to add, subtract, multiply and divide polynomial functions. In addition to video lessons, we provide quizzes to help you assess your comprehension of the material. There is also a lesson that focuses on providing practice problems to help you apply polynomial division concepts. After completing this chapter, you should be able to:

- Graph quartics, cubics and quintics
- Explain local minimums and maximums
- Evaluate polynomials with several variables
- Use long and synthetic division to divide polynomials
- Add, multiply and subtract polynomials that have several variables

Video | Objective |
---|---|

How to Graph Cubics, Quartics, Quintics and Beyond | Explain how to graph polynomials and how they are influenced by the lead coefficient. Define local maximum and local minimum. |

How to Add, Subtract and Multiply Polynomials | Explain methods for subtracting, multiplying and adding polynomials. |

How to Divide Polynomials with Long Division | Describe how to use long division to divide polynomials. |

How to Use Synthetic Division to Divide Polynomials | Demonstrate dividing polynomials through synthetic division. |

Dividing Polynomials with Long and Synthetic Division: Practice Problems | Get practice dividing polynomials with long and synthetic division. |

Operations with Polynomials in Several Variables | Evaluate a polynomial in several variables for given values of the variables. Identify the coefficients and the degrees of the terms of a polynomial and the degree of a polynomial. Demonstrate how to add, subtract and multiply polynomials with several variables. |

### 1. How to Graph Cubics, Quartics, Quintics and Beyond

Finding the graph of a polynomial isn't too hard. If you can graph, you already know the major steps! With a couple rules and helpful memorizing tools, you will be graphing polynomials in no time!

### 2. How to Add, Subtract and Multiply Polynomials

Adding, subtracting and multiplying polynomials are, basically, the same as adding, subtracting and multiplying numbers. They only difference is that we have a pesky variable to worry about, but this video will show you that's no problem, so no worries! This method has worked for many of my students, and I think it will work for you, too!

### 3. How to Divide Polynomials with Long Division

Arithmetic long division and polynomial long division are very similar. Yes, it's a long process, but once you have the rhythm you will get every problem correct!

### 4. How to Use Synthetic Division to Divide Polynomials

Synthetic division is a 'short-cut' way of dividing a polynomial by a monomial. You still need to know long division, sorry, but this method is way fun when you're dividing by a monomial!

### 5. Dividing Polynomials with Long and Synthetic Division: Practice Problems

Let's look at some more polynomial division problems. We will use long division and synthetic division, but this time we will have a couple of more involved problems. So, get out some paper and a pencil and let's begin!

### 6. Operations with Polynomials in Several Variables

In this video lesson, you will learn how to handle and work with polynomials that have more than one variable. This is important because in math you sometimes have to work with several variables at the same time.

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### Other Chapters

Other chapters within the Algebra I: High School course

- High School Algebra: Solving Math Word Problems
- High School Algebra: Percent Notation
- High School Algebra: Calculations, Ratios, Percent & Proportions
- High School Algebra: Real Numbers
- High School Algebra: Exponents and Exponential Expressions
- High School Algebra: Properties of Exponents
- High School Algebra: Radical Expressions
- High School Algebra: Algebraic Expressions and Equations
- High School Algebra: Algebraic Distribution
- High School Algebra: Properties of Functions
- High School Algebra: Working With Inequalities
- High School Algebra: Linear Equations
- High School Algebra: Factoring
- High School Algebra: Quadratic Equations
- High School Algebra: Graphing and Factoring Quadratic Equations
- High School Algebra: Rational Expressions
- High School Algebra: Matrices and Absolute Value
- High School Algebra: Data, Statistics, and Probability
- Teacher Resources for High School Algebra