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Ch 20: TExES Physics/Math 7-12: Polynomials

About This Chapter

In preparation for the TExES Physics/Mathematics 7-12 certification exam, review how to evaluate, graph, add, subtract, multiply and divide polynomials through this series of lesson videos.

TExES Physics/Math 7-12: Polynomials - Chapter Summary

This chapter, part of a preparation course for the TExES Physics/Mathematics 7-12 exam, is comprised of a series of lesson videos, worksheets and quizzes on the operations of polynomials. After completing this chapter you should be able to:

  • Evaluate polynomials in functional notation
  • Graph polynomials and perform basic transformations
  • Graph cubics, quartics and quintics
  • Add, subtract, multiply, synthetically divide and long divide with polynomials
  • Use Pascal's triangle
  • Explain binomial theorem
  • Perform operations with polynomials in multiple variables

Use the lesson worksheets to reinforce the information presented in the lesson videos and the lesson quizzes to find areas of weakness. Fortify these areas by returning to the lesson videos with video tags linked to the key points of the videos. If at any time you come up with questions during this chapter, be sure to ask our instructors for clarification so that you can master the material presented.

10 Lessons in Chapter 20: TExES Physics/Math 7-12: Polynomials
Test your knowledge with a 30-question chapter practice test
How to Evaluate a Polynomial in Function Notation

1. 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.

Understanding Basic Polynomial Graphs

2. 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

3. 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.

How to Graph Cubics, Quartics, Quintics and Beyond

4. 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!

How to Add, Subtract and Multiply Polynomials

5. 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!

Pascal's Triangle: Definition and Use with Polynomials

6. Pascal's Triangle: Definition and Use with Polynomials

Pascal's Triangle is defined and discussed briefly. Following the introduction to the triangle, its use in expanding polynomial powers is elaborated with examples.

The Binomial Theorem: Defining Expressions

7. 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.

How to Divide Polynomials with Long Division

8. 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

9. 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!

Operations with Polynomials in Several Variables

10. 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.

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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