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Ch 16: Higher-Degree Polynomials: Homeschool Curriculum

About This Chapter

The Higher-Degree Polynomials unit of this High School Precalculus Homeschool course is designed to help homeschooled students learn about higher-degree polynomial functions. Parents can use the short videos to introduce topics, break up lessons and keep students engaged.

Who's it for?

This unit of our High School Precalculus Homeschool course will benefit any student who is trying to learn to solve higher-degree polynomial functions. There is no faster or easier way to learn about precalculus. Among those who would benefit are:

  • Students who require an efficient, self-paced course of study to learn to add, subtract and multiply polynomials as well as use long division to divide polynomials.
  • Homeschool parents looking to spend less time preparing lessons and more time teaching.
  • Homeschool parents who need a precalculus curriculum that appeals to multiple learning types (visual or auditory).
  • Gifted students and students with learning differences.

How it works:

  • Students watch a short, fun video lesson that covers a specific unit topic.
  • Students and parents can refer to the video transcripts to reinforce learning.
  • Short quizzes and a Higher-Degree Polynomials unit exam confirm understanding or identify any topics that require review.

Higher-Degree Polynomials Unit Objectives:

  • Use quadratic form to factor polynomials.
  • Use the rational zero theorem and synthetic division to factor polynomials.
  • Learn about the factor and remainder theorems.
  • Identify polynomials that can be written in quadratic form.
  • Explain the fundamental theorem of algebra.

9 Lessons in Chapter 16: Higher-Degree Polynomials: Homeschool Curriculum
Test your knowledge with a 30-question chapter practice test
Solving Higher Degree Polynomials

1. Solving Higher Degree Polynomials

After watching this video lesson, you will be able to solve polynomials where the degree is three or higher. Learn the technique that you can use to solve any one of these polynomials.

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!

Factoring Polynomials Using Quadratic Form: Steps, Rules & Examples

3. 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.

How to Divide Polynomials with Long Division

4. 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

5. 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!

Remainder Theorem & Factor Theorem: Definition & Examples

6. 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.

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!

Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division

8. 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.

Fundamental Theorem of Algebra: Explanation and Example

9. 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.

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.
Not Taken

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Other Chapters

Other chapters within the High School Precalculus: Homeschool Curriculum course

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