Hi everyone! Read through the material below, watch the videos, and send me your questions.

Lesson 12: Polynomial and Rational Inequalities

Topic: This lesson covers Chapter 12 in the book, Polynomial and Rational Inequalities.

WeBWorK: There are two WeBWorK assignments on today’s material: Polynomials - Inequalities, and Rational Functions - Inequalities.

Introduction to polynomial inequalities

Definition. A polynomial inequality is an inequality (which means it uses one of these: $<,\leq,>,\geq$ instead of an equals sign) with a polynomial on each side

Example 1: $x^2-3x-4\geq 0$

We’re interested in solving these inequalities, which means answering the question: “For which real numbers x is the inequality true?”

Now let’s look at the same example, and see how to solve it without looking at the graph:

Example 2: Solve $x^{4}-x^{2}>5\left(x^{3}-x\right)$

Example 2, concluded:

Rational inequalities

What happens if we allow rational functions instead of just polynomials?

Example 3: Solve $\frac{x^{2}-5 x+6}{x^{2}-5 x} \geq 0$

Good job! You are now ready to practice on your own. Take a look at the WeBWorK assignment, and don’t forget to use the “Ask for Help” button if you get stuck.

Here are more video resources if you’d like to see additional examples.

ASSIGNMENT: Watch videos, try webwork.

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