Solve and Graph Polynomial Inequalities

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 .