1. Polynomial Inequalities in One Variable
Let P(x) be any polynomial. Then P(x) < 0 and P(x) > 0 are called polynomial inequalities.
To solve polynomial inequalities:
Use a sign graph of P(x)
Analyze a graph of P(x):
P(x) > 0 when the graph is above the x-axis
P(x) < 0 when the graph is below the x-axis

2. Find the zeros of the polynomial
Plot the zeros on a number line
Test for the signs of P(x) in each interval
The solution of P(x) < 0 is x < -1 or 0 < x < 3

3. Activity
Explain why this product should not change sign at x = 1.

4. Find the zeros:

5. Example 3. Solve
Find the zeros of all linear factors in the numerator and denominator:
The solution of f(x) < 0 is –2 < x < 4 or x = 5

6. Example 4. Solve
by using a graphing calculator.