Polynomial and rational functions

Linear and quadratic functions are the simplest polynomial functions. In this chapter, we study polynomials of any degree, such as ${x^3-4x}$ or ${2x^5+x^2-7}$. We learn how their graphs look, how to divide them, and how to find their zeros.

A rational function is a fraction with polynomials in the numerator and the denominator. At the end of the chapter, you will learn to graph these functions, too.

This chapter covers the following topics:

Polynomial functions and their graphs

End behavior, zeros and their multiplicity, turning points, the intermediate value theorem, and sketching graphs of polynomials.

Dividing polynomials

Long division and synthetic division of polynomials, and the remainder and factor theorems.

Zeros of polynomials

The rational zeros theorem, finding all zeros of a polynomial, the fundamental theorem of algebra, and complex zeros.

Rational functions

The domain of a rational function, vertical, horizontal, and slant asymptotes, holes, and sketching graphs.

Practice questions

Practice problems on every section of this chapter, with full step-by-step solutions.

Before you start

This chapter uses factoring from Chapter 1, quadratic equations and complex numbers from Chapter 2, and graphs of functions from Chapter 3.