(6) ­ The Rational Root Theorem.notebook March 16, 2015Bell work

Find the other zeros of

f(x) = x5 - 4x4 - 13x3 + 52x2 + 36x - 144

given that f (4) = 0.

2.6 The Rational Root Theorem

If f (x) = anxn + ... + a1x + a0 has integer coefficients, then every rational zero of f has the

following form:

p factor of constant term a0 q factor of leading coeffiecient an

__ = __________________________________________________________=__

If f (x) = anxn + ... + a1x + a0 has integer coefficients, then every rational zero of f has the

following form:

p factor of constant term a0 q factor of leading coeffiecient an

(6) ­ The Rational Root Theorem.notebook March 16, 2015

List the possible rational zeros of

f (x) = x3 + 2x2 - 11x + 12.

List the possible rational zeros of f (x) = 2x4 + 5x3 - 18x2 - 19x + 8.

(6) ­ The Rational Root Theorem.notebook March 16, 2015

Finding zeros when the leading

coefficient =1

Find all real zeros of

f(x)= x3 - 8x2 +11x +20

Step 1: List the possible rational zeros.

Step 2: Test the zeros using synthetic division

Step 3: Factor the trinomial

Find all real zeros of

f(x)= x3 - 8x2 +5x +14

(6) ­ The Rational Root Theorem.notebook March 16, 2015

Assignment:

p. 132 # 12-18 even