1. Section 1.6 Polynomial and Rational Inequalities

2. Polynomial Inequalities We said that we can find the solutions (a.k.a. zeros) of a polynomial by setting the polynomial equal to zero and solving. We are going to use this skill to solve inequalities such as:

3. Solving Quadratic Inequalities Factor Identify the zeros (critical points) There are now 3 intervals: (-∞,-3), (-3,4), and (4,∞). We will test these three intervals to see which parts of this function are less than (negative) or greater than (positive) zero.

4. Testing Intervals To test, pick a number from each interval and evaluate Instead of evaluating, we can also just check the signs of each factor in our factored form of the polynomial. Solution: (-∞,-3) U (4,∞)

5. Recap of Steps Factor and solve the quadratic to find the critical points Test each interval Determine if (+) or (-) values are desired

6. Solve the Inequality Solution:

7. x 2 – 2x ≥ 1 Solution:

8. x 2 + 2x ≤ -3 No Real Solutions Test any number to find out if all numbers are true or false.

9. Solve the rational inequality Restrictions?

10. Solving Rational Inequalities Solution: (-∞,-8) U (-1,8) Restrictions?

12. Test any number… it’s either all positive, or all negative.

13. Restrictions? Solve

14. No Restrictions

15. Solve Restrictions?