About This Chapter
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.
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.
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. 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.
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!
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!
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.
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!
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.
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.
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Other chapters within the High School Precalculus: Homeschool Curriculum course
- Graphing Linear Equations: Homeschool Curriculum
- Solving & Graphing Inequalities: Homeschool Curriculum
- Absolute Value Expressions: Homeschool Curriculum
- Graphing Complex Numbers: Homeschool Curriculum
- Solving Linear Systems: Homeschool Curriculum
- Linear Models: Homeschool Curriculum
- Quadratics: Homeschool Curriculum
- Quadratic Functions & Equations: Homeschool Curriculum
- Geometry Basics: Homeschool Curriculum
- Functions for Precalculus: Homeschool Curriculum
- Using Function Operations: Homeschool Curriculum
- Recognizing Graph Symmetry: Homeschool Curriculum
- How to Graph Functions: Homeschool Curriculum
- Rate of Change: Homeschool Curriculum
- Polynomial Functions: Homeschool Curriculum
- Difference Quotients in Precalculus: Homeschool Curriculum
- Working with Rational Expressions: Homeschool Curriculum
- Evaluating Logarithmic Functions: Homeschool Curriculum
- Functions in Trigonometry: Homeschool Curriculum
- Using Trigonometric Graphs: Homeschool Curriculum
- Trigonometric Equations: Homeschool Curriculum
- Basic Trigonometric Identities: Homeschool Curriculum
- Laws of Sine & Cosine: Homeschool Curriculum
- Graphing Piecewise Functions: Homeschool Curriculum
- Vectors & Matrices: Homeschool Curriculum
- Mathematical Sequences: Homeschool Curriculum
- Identifying Conic Sections: Homeschool Curriculum
- Parametric Equations: Homeschool Curriculum
- Continuity: Homeschool Curriculum
- Limits in Precalculus: Homeschool Curriculum
- Groups & Sets in Algebra: Homeschool Curriculum