Ch 6: Holt McDougal Algebra 2 Chapter 6: Polynomial Functions

About This Chapter

The Polynomial Functions chapter of this Holt McDougal Algebra 2 Textbook Companion Course helps students learn essential algebra lessons on polynomial functions. Each of these simple and fun video lessons is about five minutes long and is sequenced to align with the Polynomial Functions textbook chapter.

How it works:

  • Identify the lessons in the Holt McDougal Algebra 2 Polynomial Functions chapter with which you need help.
  • Find the corresponding video lessons within this companion course chapter.
  • Watch fun videos that cover the polynomial functions topics you need to learn or review.
  • Complete the quizzes to test your understanding.
  • If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.

Students will learn:

  • Adding, subtracting, multiplying and dividing polynomials
  • Factoring by grouping
  • Remainder and factor theorems
  • Solving perfectly cubed equations
  • Finding rational zeros
  • The fundamental theorem of algebra
  • Writing polynomial equations
  • Graphing cubics, quartics and quintics

Holt McDougal is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.

16 Lessons in Chapter 6: Holt McDougal Algebra 2 Chapter 6: Polynomial Functions
Test your knowledge with a 30-question chapter practice test
What are Polynomials, Binomials, and Quadratics?

1. What are Polynomials, Binomials, and Quadratics?

What do polynomials, binomials, and quadratics have in common? What are their differences? How can you identify each of them? Watch this video lesson to find the answers.

How to Add, Subtract and Multiply Polynomials

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!

How to Evaluate a Polynomial in Function Notation

3. How to Evaluate a Polynomial in Function Notation

This lesson will review how to evaluate polynomials in function notation. Along with an analogy to explain the process, examples will be given and worked during the lesson.

What is the Binomial Theorem?

4. What is the Binomial Theorem?

While the F.O.I.L. method can be used to multiply any number of binomials together, doing more than three can quickly become a huge headache. Luckily, we've got the Binomial Theorem and Pascal's Triangle for that! Learn all about it in this lesson.

How to Divide Polynomials with Long Division

5. 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!

How to Use Synthetic Division to Divide Polynomials

6. 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!

Dividing Polynomials with Long and Synthetic Division: Practice Problems

7. 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!

Factoring By Grouping: Steps, Verification & Examples

8. Factoring By Grouping: Steps, Verification & Examples

How do you factor an expression if all the terms don't share a common factor? Grouping! In this lesson, we'll learn how to use grouping to help factor expressions.

Remainder Theorem & Factor Theorem: Definition & Examples

9. 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.

How to Solve Perfectly Cubed Equations

10. How to Solve Perfectly Cubed Equations

Watch this video lesson so you can identify perfectly cubed equations. Learn about the formula that helps you factor them and then to solve them. See how easy it is to use these formulas.

Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division

11. 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.

The Irrational Root Theorem: Definition & Application

12. The Irrational Root Theorem: Definition & Application

This lesson describes the irrational root theorem and how it may be used to find additional roots for a polynomial. The irrational root theorem works only if the coefficients of the polynomial are rational.

Fundamental Theorem of Algebra: Explanation and Example

13. 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.

Using Rational & Complex Zeros to Write Polynomial Equations

14. 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.

How to Graph Cubics, Quartics, Quintics and Beyond

15. 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!

Basic Transformations of Polynomial Graphs

16. 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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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