1. Warm – up #5

3. Homework Log Fri 1/8 Lesson 5 – 4 Learning Objective: To apply Rational Zeros Theorem Hw: #507 Pg. 302 #1 – 19 odd

4. 1/8/16 Lesson 5 – 4 Rational Zeros Day 1 Advanced Math/Trig

5. Learning Objective To apply the Rational Zeros Theorem To apply Bound Theorem

6. Rational Zeros Theorem

8. Give the set of possible rational zeros of P(x)

10. Bounds Theorem Using synthetic division on poly with real coeff & lead coeff is positive: (1) If c is a positive real, & all #s in last row are non-negative, c is an upper bound (no zeros > c) (2) If c is a negative real, & the #s in last row alternate in sign, c is a lower bound (no zeros < c) (0 can be written as +0 or -0)

11. a) Find smallest possible integer that bounds theorem detects as an upper bound for the zeros of 1 3 – 7 15 – 35 3 2 – 4 3– 1 3 3 2 21 28 Stop when neg. All non- neg. 3 is an upper bound

12. b) Find the negative integer nearest zero that bounds theorem detects as a lower bound for the zeros of – 1 3 – 7 15 – 35 3 – 10 25 – 60 Alt. signs –1 is a lower bound

13. Find upper & lower bounds for the zeros of 1 1 – 1 – 4 – 2 – 13 10– 4 2 11 – 2 3 12 2 4– 1 4 138 30107 – 11– 2 1– 32 1– 48 – 2665 – 6– 1 4 is upper bound –3 is lower bound Stop when neg. Stop when not alternating

14. Find upper & lower bounds for the zeros of 1 1 1 – 11 1 – 10 12– 9 2 13 – 5 3 14 1 42 – 1 10–12 – 21– 1– 9 – 3 1– 2–5 – 4 1– 31 2 3 is upper bound – 4 is lower bound Stop when neg. Stop when not alternating

15. Ticket Out the Door

16. Homework #507 Pg. 302 #1 – 19 odd