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Ch 16: Advanced Polynomial Functions: Precalculus Lesson Plans

About This Chapter

The Advanced Polynomial Functions: Precalculus chapter of this course is designed to help you plan and teach about the higher degree polynomials and related mathematical theorems in your classroom. The video lessons, quizzes and transcripts can easily be adapted to provide your lesson plans with engaging and dynamic educational content. Make planning your course easier by using our syllabus as a guide.

Weekly Syllabus

Below is a sample breakdown of the Advanced Polynomial Functions: Precalculus chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.

Day Topics Key Terms and Concepts Covered
Monday How to solve advanced polynomials Degree 3 and higher polynomials, rational roots theorem, multiplying polynomials, subtracting polynomials, and adding polynomials
Tuesday Quadratic form Standard form, changing form, factoring, quadratic form, and au^2 + bu + c
Wednesday Dividing polynomials: Part I Quotient, dividend, polynomial long division, synthetic division, coefficient, and leading coefficient
Thursday Dividing polynomials: Part II Division procedure, remainder theorem, factor theorem, and when to use synthetic division vs. long division
Friday Other theorems Irrational zero, rational zero, f(x) = 0, rational zeros theorem, fundamental theorem of algebra, repeated solutions, complex solutions, and conjugate pairs

9 Lessons in Chapter 16: Advanced Polynomial Functions: Precalculus Lesson Plans
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.

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Other Chapters

Other chapters within the High School Precalculus Syllabus Resource & Lesson Plans course

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