Warm Up #2 Factor completely. 2. 2x2 – 5x – 3 1. x2 – x – 12

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Presentation transcript:

Warm Up #2 Factor completely. 2. 2x2 – 5x – 3 1. x2 – x – 12 3. Use synthetic division to divide 2x3 – 3x2 – 18x – 8 by x – 4. 4 2 -3 -18 -8 8 8 20 2 5 2

EXAMPLE 1 List possible rational zeros List the possible rational zeros of f using the rational zero theorem. a. f (x) = x3 + 2x2 – 11x + 12 Factors of the constant term: + 1, + 2, + 3, + 4, + 6, + 12 Factors of the leading coefficient: + 1 Possible rational zeros: + , + , + , + , + , + 1 2 3 4 6 12 Simplified list of possible zeros: + 1, + 2, + 3, + 4, + 6, + 12

EXAMPLE 1 List possible rational zeros b. f (x) = 4x4 – x3 – 3x2 + 9x – 10 Factors of the constant term: + 1, + 2, + 5, + 10 Factors of the leading coefficient: + 1, + 2, + 4 + , + , + , + , + , + , + , + , + , + , + Possible rational zeros: 1 2 5 10 4 + 10 Simplified list of possible zeros: + 1, + 2, + 5, + 10, + , + , + 5 2 1 4 +

GUIDED PRACTICE for Example 1 List the possible rational zeros of f using the rational zero theorem. 1. f (x) = x3 + 9x2 + 23x + 15 Factors of 15: Factors of 1: ANSWER + 1, + 3, + 5 + 15

GUIDED PRACTICE for Example 1 List the possible rational zeros of f using the rational zero theorem. 2. f (x) =2x3 + 3x2 – 11x – 6 Factors of -6: Factors of 2:

EXAMPLE 2 Find zeros when the leading coefficient is 1 Find all real zeros of f (x) = x3 – 8x2 + 11x + 20. SOLUTION Use the graphic display calculator y1 = f(x) y2 = 0

Zeros are 1 , 6 , -3 GUIDED PRACTICE for Example 2 Find all real zeros of the function. 3. f (x) = x3 – 4x2 – 15x + 18 Zeros are 1 , 6 , -3

GUIDED PRACTICE for Example 2 Find all real zeros of the function. 4. f (x) = x3 – 8x2 + 5x+ 14

1 -5 9 -5 8 12

Factored form Now solve the last quadratic for the imaginary solutions. There are 5 solutions!

Class/Homework Assignment: Worksheet 5.6 ( #1 – 19 odd)