Course: College Algebra
Topic: Equations and Inequalities
Subtopic: Polynomial and Rational Inequalities


In Calculus I you are required to solve inequalities on f(x), f'(x) (the first derivative of f), and f"(x) (the second derivative of f) all in one problem. Since f(x) and its derivatives could be linear, polynomial, rational, or otherwise, it is helpful to be proficient in solving inequalities involving a variety of functions.

The main goal is to determine when the function is positive and when it is negative. This can be accomplished graphically or algebraically. If algebraically, the sign chart method of solving these inequalities is the efficient and reliable, but most texts use a test point method instead. Either works and we can compare and contrast the methods in class so you can learn the method you prefer.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: polynomial inequality, rational inequality, sign chart, test point

Text Notes

Practice solving a variety of polynomial and rational inequalities both algebraically and graphically. Concentrate on the pure process without having to expand to applications.

You may SKIP any "curve fitting" and "regression" examples/problems in this section and throughout the course.

Mini-Lectures and Examples

STUDY: Polynomial and Rational Inequalities

Supplemental Resources (optional)

If you need supplemental tutorial videos with examples relevant to this section go to James Sousa's MathIsPower4U and search for topics:
"Solving Polynomial Inequality"
"Solving Rational Inequalities"

rev. 2020-10-10