# Ch 3: Understanding Polynomial Functions

### About This Chapter

## Understanding Polynomial Functions - Chapter Summary

This chapter contains lessons on understanding polynomial functions. Take a look at information on the definition and examples of factor theorem and remainder theorem, discover operations that can be used with polynomials in several variables, and go over the explanation of the fundamental theorem of algebra. Other lesson topics include:

- Addition, subtraction and multiplication of polynomials
- Polynomial division using long division
- Polynomial division using synthetic division
- Use of the rational zeros theorem and synthetic division to find rational zeros
- Writing polynomial equations using rational and complex zeros
- Examples of the long-run and short-run behavior of polynomials
- Basic polynomial graphs' translation
- Graphing of cubics, quintics, quartics and more

Our instructors host these short video lessons, each lasting 5-10 minutes on average. Whenever you have a few minutes, log on using your mobile device and complete one or more lessons. Track your progress on the dashboard. With each lesson, we include a short self-assessment quiz to check your understanding.

### 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. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. Short Run & Long Run Behavior of Polynomials: Definition & Examples

Watch this video lesson to learn how you can use the graph of a polynomial to help you explain the polynomial function. Learn how to explain the behavior of the polynomial at the origin and at the far ends.

### 11. Understanding Basic Polynomial Graphs

This lesson will cover understanding basic polynomial graphs. The lesson focuses on how exponents and leading coefficients alter the behavior of the graphs.

### 12. Basic Transformations of Polynomial Graphs

The basic transformations for a graph are movement up and down, left and right, pinched or stretched graphs, and flipped graphs. This lesson will review how to accomplish each of these transformations.

### 13. 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!

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### Other Chapters

Other chapters within the STAAR Algebra II: Test Prep & Practice course

- Complex and Imaginary Numbers
- Calculating & Simplifying Exponential Expressions
- Solving Algebraic Equations Overview
- Operations with Radical Expressions
- The Basics of Functions
- Graphing Functions Overview
- Solving & Graphing Systems of Equations
- Solving & Graphing 1 & 2 Variable Inequalities
- Solving & Graphing Quadratics
- Quadratics & Higher Order Polynomials
- Solving Exponential & Logarithmic Functions
- Absolute Value Equations
- Rational Functions & Expressions
- About the STARR Tests
- STAAR Algebra II Flashcards