Warm – up #5

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

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

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

Rational Zeros Theorem

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

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)

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

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 – – 60 Alt. signs –1 is a lower bound

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

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

Ticket Out the Door

Homework #507 Pg. 302 #1 – 19 odd