1. Agenda – Jan 6  Do Now  Review Reading  Notes: Rational Root Theorem  Work Time Due NEXT CLASS: Rational Root Theorem By the end of today’s class, you will be able to … Identify and test possible roots of a polynomial function Get a handout please In dress code In your seat Due Today: Reading – Rational Root Theorem

2. 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 is a tool for predicting the values of Rational Roots. The theorem says:

4. Are the coefficients all integers? Then possible rational roots are I where

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

6. So the possible zeros are: I

7. Substitute each possible rational roots into f(x). If the value is a root, then f(value) = 0

8. Continue testing possible rational roots for f(x).

9. Continue testing possible rational roots for f(x).

10. Continue testing possible rational roots for f(x).

11. so must be a factor of f(x). Use long or synthetic division to further factor f(x)

12. Simplify! Simplify further!

15. The Rational Root Theorem says: