# Ch 5: Polynomial Functions of a Higher Degree

### About This Chapter

## Polynomial Functions of a Higher Degree - Chapter Summary and Learning Objectives

The lessons in this chapter will teach you to work with higher degree polynomials. You'll learn to add, subtract, multiply and divide polynomials as well as how to identify them in quadratic form. Other lessons cover factoring with polynomials and writing equations. This chapter is designed to teach you how to:

- Add, subtract and multiply polynomials
- Work with polynomials in quadratic form
- Understand and utilize the remainder and the factor theorems
- Find rational zeros
- Write polynomial equations with rational and complex zeros

Videos | Objectives |
---|---|

How to Add, Subtract and Multiply Polynomials | Perform basic functions with polynomials. |

Factoring Polynomials in Quadratic Form of Degree 4 or Higher | Identify and evaluate polynomials in quadratic form. |

How to Divide Polynomials with Long Division | Divide polynomials utilizing long division. |

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

Remainder Theorem and Factor Theorem | State the theorems and use them to find factors of polynomials. |

Dividing Polynomials with Long and Synthetic Division: Practice Problems | Gain skill in performing these operations. |

Finding Rational Zeros Using the Rational Zero Theorem and Synthetic Division | Factor polynomials using the rational zero theorem and synthetic division. |

Fundamental Theorem of Algebra | Determine how many solutions a polynomial has based on the degree of the polynomial. |

Using Rational and Complex Zeros to Write Polynomial Equations | Write a polynomial equations using given zeros of a function and the concept of complex conjugate pairs. |

### 1. 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!

### 2. Factoring Polynomials Using Quadratic Form: Steps, Rules & Examples

Factoring a polynomial of degree 4 or higher can be a difficult task. However, some polynomials of higher degree can be written in quadratic form, and the techniques used to factor quadratic functions can be utilized.

### 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. Remainder Theorem & Factor Theorem: Definition & Examples

In this lesson, you will learn about the remainder theorem and the factor theorem. You will also learn how to use these theorems to find remainders and factors of polynomials.

### 6. 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!

### 7. Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division

After completing this lesson, you will know what the rational zeros theorem says. You will also know how to apply this theorem to find zeros of polynomial functions.

### 8. Fundamental Theorem of Algebra: Explanation and Example

In this lesson, you will learn what the Fundamental Theorem of Algebra says. You will also learn how to apply this theorem in determining solutions of polynomial functions.

### 9. Using Rational & Complex Zeros to Write Polynomial Equations

In this lesson, you will learn how to write a polynomial function from its given zeros. You will learn how to follow a process that converts zeros into factors and then factors into polynomial functions.

### Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the Math 105: Precalculus Algebra course

- Mathematical Modeling
- Linear Equations & Inequalities
- Quadratic Functions
- Rational Expressions and Functions
- Absolute Value Equations & Inequalities
- Complex Numbers
- Geometry Basics
- Functions Overview
- Function Operations
- Graph Symmetry
- Exponential and Logarithmic Functions
- Introduction to the Derivative
- Studying for Math 105