# Precalculus : Solve and Graph Polynomial Inequalities

## Example Questions

### Example Question #1 : Solving Polynomial And Rational Inequalities

What is the solution to the following inequality?

Explanation:

First, we must solve for the roots of the cubic polynomial equation.

We obtain that the roots are .

Now there are four regions created by these numbers:

• . In this region, the values of the polynomial are negative (i.e.plug in  and you obtain

• . In this region, the values of the polynomial are positive (when , polynomial evaluates to )

•  . In this region the polynomial switches again to negative.

• . In this region the values of the polynomial are positive

Hence the two regions we want are  and .