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Chapter 6 Final Touches

Chapter 6 Final Touches. 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!!!. If “it” goes in evenly, it’s a. If “it” goes in evenly, it’s a. FACTOR. If “it” goes in evenly, it’s a. FACTOR

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Chapter 6 Final Touches

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  1. Chapter 6Final 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. If “it” goes in evenly, it’s a 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: • Solve:

  16. Back to finding all the roots • Solve: • Solve: • Solve:

  17. Fundamental Theorem of Algebra • (Corollary) nth 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 • 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

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