# Ch 16: Higher-Degree Polynomial Functions

Watch online math video lessons and take self-assessment quizzes to learn about the rational zero theorem, synthetic division, the fundamental theorem of algebra and more.

## Higher-Degree Polynomial Functions - Chapter Summary and Learning Objectives

Instructors teaching this chapter on higher-degree polynomials, such as cubics, quartics and quintics, introduce you to methods for factoring these types of functions and solving polynomial equations. Practice problems are also included to help you get the hang of determining which technique to use and when, along with lessons showing you the practical applications of the fundamental theorem of algebra. Once you've worked your way through this chapter, you should be able to:

• Perform basic arithmetic operations on polynomials
• Convert higher-degree polynomials into quadratic form
• Use synthetic and long division to factor higher-degree polynomials
• Apply the remainder, factor and rational zero theorems
• Determine the number of solutions to a polynomial function

Video Objectives
Solving Polynomials of Degree Greater Than or Equal to Three Learn how to solve polynomial equations of the third degree and higher.
How to Add, Subtract and Multiply Polynomials Understand how to perform arithmetic operations on polynomials.
Factoring Polynomials Using Quadratic Form: Steps, Rules & Examples Identify higher-degree polynomials that can be written in quadratic form. Learn how to factor them.
How to Divide Polynomials with Long Division Explore techniques for performing long division on higher-degree polynomials.
How to Use Synthetic Division to Divide Polynomials Use synthetic division to divide a polynomial by a monomial.
Remainder Theorem & Factor Theorem: Definition & Examples Examine how the remainder and factor theorems can be used as an alternative to synthetic or long division.
Dividing Polynomials with Long and Synthetic Division: Practice Problems Get extra practice determining when and how to use synthetic or long division.
Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division Explore the uses of the rational zero theorem and synthetic division to factor polynomials.
Fundamental Theorem of Algebra: Explanation and Example Learn how a polynomial's degree can be used to determine the number of solutions it has.

9 Lessons in Chapter 16: Higher-Degree Polynomial Functions
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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