1. Polynomial Inequalities in One Variable
Section 3-2
Polynomial Inequalities in One Variable

2. Polynomial Inequalities
Let P(x) be any polynomial. Then P(x) < 0 and P(x) > 0 are called polynomial inequalities. There are two ways to solve a polynomial inequality.

3. Two ways to solve a Polynomial Inequality
Method 1: Use a sign graph of P(x)
Using a sign graph is an easy way to solve a polynomial inequality if the polynomial is factorable.

4. Using a Sign Analysis to Solve Polynomial Inequalities
Recall…
To perform a sign analysis of a polynomial P(x), you test one value of x from each of the intervals determined by the zeros of P(x). Then you determine the sign of P(x) in each of these intervals.

5. Two ways to solve a Polynomial Inequality
Method 2: Analyze a graph of P(x).
Note that P(x) > 0 when the graph is ABOVE the x-axis and
P(x) < 0 when the graph is BELOW the x-axis

6. Using the Graphing Calculators to Solve Polynomial Inequalities
Put a plus sign where the graph is above the x axis
Put a minus sign where the graph is below the x axis
If P(x)>0 you want plus signs
If P(x)<0 you want minus signs

7. Example
Solve using Sign Analysis
Solve Using the Graphing Calculator

8. Activity
Complete Activity on page 101.

9. Effect of a Squared Factor
This activity shows that not all polynomials change sign at a zero.
A polynomial P(x) will NOT change sign at a zero c if c corresponds to the squared factor (x – c)2.

10. Example
Solve by Sign Analysis
Solve by using the graphing calculator

11. Solving Polynomial Inequalities
You must use the sign analysis when you have a polynomial inequality that is a fraction.
See example 3 p. 102

12. Examples
Solve: