Solving Polynomial Inequalities

In this lesson, we will learn how to solve polynomial inequalities. From the Intermediate Value Theorem, we can state that function values are not going to change sign between consecutive real zeros. This means that the function values are either always positive or always negative when we are between consecutive real zeros. This allows us to solve the inequality by first rearranging the inequality so that the right side is zero. We will then replace the inequality symbol with an equality symbol and solve the resulting equation. From there, we will use the real solutions to our equation, which are known as the critical values, to split the number line up into intervals. At that point, we can use test values or make a sign chart to find out if our function is positive or negative in each interval. Once that is done, we can determine the solution of the inequality based on its sign in each interval. Lastly, our endpoints would be included for a non-strict inequality and excluded for a strict inequality.