Today’s Agenda – Feb 3

1. Pre-Calculus 1 Today’s Agenda – Feb 3 Due TODAY:HW #51 • Graphing Polynomials - Redux Due TOMORROW: HW #52 • Rational Root Theorem • 1. Silent Do Now • Notes • Rational Root Theorem 3. Work Time Questions/Summary SWBAT… • Apply rational root theorem to identify possible roots of a polynomial • Use synthetic/long division or factor theorem to test possible roots

2. FACTOR THIS… Without more information, our best hope of factoring this cubic function is to guess and check. There is a better way…

3. The Rational Root Theorem The Rational Root Theorem is a tool for predicting the values of Rational Roots. The theorem says:

4. Apply theRational Root Theorem Are the coefficients all integers? Then possible rational roots are I where

5. Apply theRational Root Theorem Factors of constant term, Factors of leading coefficient , All possible rational roots of the form are: I

6. Apply theRational Root Theorem So the possible zeros are:I

7. Check with Factor Theorem Substitute each of our possible rational roots into f(x). If the value is a root, then f(value) = 0

8. Check with Factor Theorem Continue testing possible rational roots for f(x).

9. Check with Factor Theorem Continue testing possible rational roots for f(x).

10. Now what? so must be a factor of f(x). Use long or synthetic division to further factor f(x)

11. Rewrite in Factored Form Simplify! Simplify further!

12. Rewrite in Factored Form

13. Rewrite in Factored Form

14. The Rational Root Theorem The Rational Root Theorem says:

15. Key Point