1. Chapter 6 Final Touches

2. Pg 325 #42-47 Determine whether each binomial is a factor of Reminds me of a “bank” Limits the ones I have to check! Of course a graph helps too!!!

3. If “it” goes in evenly, it’s a

4. FACTOR

5. If “it” goes in evenly, it’s a FACTOR We know the remainder is 0

6. Ultimate Goal To solve polynomials To graph polynomials If we can get the polynomial in factored form, then life is pretty easy!

7. Tool to help find factors Long Division – Always works Synthetic Division – Works with linear factors Especially when written in the form (x-a)

8. Tool to help find factors We need a BANK to limit the choices RATIONAL ROOT THEOREM If your polynomial is in standard form and If your polynomial has integer coefficients Then the bank consists of The possible rational roots are found in the bank

9. Example List the possible rational roots for

10. Before we extend this…

11. BOGO, new perspective Irrational Root Theorem – If the is a root, then is also a root – If is a root, then is also a root Imaginary Root Theorem – If is a root, then is also a root They are called conjugates of each other!

12. Examples Given the polynomial, find the other roots

13. Intermission Stand up and stretch for 1 minute Then use your calc to answer pg 318 #49

14. Back to finding all the roots Solve:

15. Back to finding all the roots Solve:

16. Back to finding all the roots Solve:

17. Fundamental Theorem of Algebra (Corollary) n th degree polynomials have exactly n roots (including real and imaginary) has 3 roots. Period. has 4 roots. Period.

18. All done! Solve

19. All done! Solve

20. Study Form a study group tonight! Do 6.5 pg 339 #4, 7, 12, 13, 17, 19, 21, 38 Do 6.6 pg 343 #10-12 Download Geist’s notes (from my website) Review Solving Quadratics Do Chap 5 Review pg. 300 #24, 27, 31, 38 Friday test: Chap 6 / part of Chap 5 Retest Monday: Review for Cumulative Tuesday: Cumulative 5-6 test Wed: Prepare for Final and take probability test Friday: 200 point Final