College Algebra & Trigonometry, 2018a

96 CHAPTER 2. POLYNOMIAL AND RATIONAL FUNCTIONS
2.3 Solution of Polynomial Inequalities by Graphing
In this section, we will combine the concepts of the previous two sections to solve
polynomial inequalities. In Section 2.2, we solved equations by graphing and
finding the x-values which made y = 0. In solving an inequality, we will be
concerned with finding the range of x values that make y either greater than or
less than 0, depending on the given problem.
Example
Solve the given inequality.
2x 3 +8x 2 +5x − 3 ≥ 0
First, we graph the function:
10
y =2x 3 +8x 2 +5x − 3
5
−3 −2 −1 1
−5
Then we identify the intervals of x-values that make the y value greater than or
equal to zero, as indicated in the problem.