# Polynomial and Rational Inequalities (3).docx - Math 1111...

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Math 1111 – Polynomial and Rational Inequalities Objectives: 1. Solve polynomial inequalities 2. Solve rational inequalities Objective 1: Solve polynomial inequalities A polynomial inequality is where a polynomial function, f(x), can be put into one of the following forms: f(x) > 0, f(x) < 0, f(x) ≥ 0, f(x) How to solve a linear inequality: 1. Get a zero on one side of the inequality. 2. Solve the equation f(x) = 0 by factoring or using the quadratic formula. These are the boundary points. 3. Graph the boundary points on a number line so that you have divided the number line into intervals. 4. Choose test points within each of the intervals. Plug in the test points into the factored form of the polynomial. Since you are only looking to see if the answer is positive or negative, there is no reason to solve the problem. 5. Write down the answer. Look at the number line. If the test point from a region satisfies the inequality then that region is part of the solution. If the test point doesn’t satisfy the inequality then ≤ 0