Ch 16: PLACE Mathematics: Polynomials

About This Chapter

As you prepare for the PLACE Mathematics exam, watch these lesson videos on polynomials. Learn how to complete mathematical operations with polynomials and review the functions and theorems vital to understanding how to work with polynomials.

PLACE Mathematics: Polynomials - Chapter Summary

When preparing for the Program for Licensing Assessments for Colorado Educators (PLACE) Mathematics, it could be helpful to review the functions of polynomials in mathematics. In this chapter, expert instructors explain how to solve mathematical operations with polynomials and discuss synthetic division, related mathematical theorems and polynomial graphs. After watching this series of lesson videos, you should have a better understanding of:

  • Addition, subtraction and multiplication with polynomials
  • Solving problems with polynomials in several variables
  • Long and synthetic division with polynomials
  • Remainder Theorem, Factor Theorem and Rational Zeros Theorem
  • The Fundamental Theorem of Algebra
  • Graphing polynomials and transformations of polynomial graphs
  • The Binomial Theorem

In addition to watching these video lessons, you can take quizzes to help you determine what topics you still need to review before taking the PLACE Mathematics. You can also print out lesson worksheets for further study. To simplify your review, use the jump feature in the video timelines to go to key topics in the lessons, or if you want another way of learning the material, read over the lesson transcripts.

PLACE Mathematics: Polynomials Objectives

PLACE Mathematics is the certification exam used in the state of Colorado to certify educators interested in teaching math. It is a paper-based exam composed of a series of multiple-choice questions, for which test takers are given four hours and 30 minutes to complete. The exam covers five key areas of math. Questions on polynomials are found in the functions and relations of mathematics area of the exam.

10 Lessons in Chapter 16: PLACE Mathematics: Polynomials
Test your knowledge with a 30-question chapter practice test
How to Add, Subtract and Multiply Polynomials

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!

Operations with Polynomials in Several Variables

2. 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.

How to Divide Polynomials with Long Division

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!

How to Use Synthetic Division to Divide Polynomials

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!

Remainder Theorem & Factor Theorem: Definition & Examples

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.

Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division

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.

Fundamental Theorem of Algebra: Explanation and Example

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.

Understanding Basic Polynomial Graphs

8. 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.

Basic Transformations of Polynomial Graphs

9. 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.

The Binomial Theorem: Defining Expressions

10. The Binomial Theorem: Defining Expressions

In this lesson, students will learn the binomial theorem and get practice using the theorem to expand binomial expressions. The theorem is broken down into its parts and then reconstructed.

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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Other Chapters

Other chapters within the PLACE Mathematics: Practice & Study Guide course

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