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

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

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

Find the zeros:

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

Example 4. Solve by using a graphing calculator.