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EXAMPLE 1 List possible rational zeros List the possible rational zeros of f using the rational zero theorem. a. f (x) = x 3 + 2x 2 – 11x + 12 Factors.

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Presentation on theme: "EXAMPLE 1 List possible rational zeros List the possible rational zeros of f using the rational zero theorem. a. f (x) = x 3 + 2x 2 – 11x + 12 Factors."— Presentation transcript:

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

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

3 GUIDED PRACTICE for Example 1 List the possible rational zeros of f using the rational zero theorem. 1. f (x) = x 3 + 9x 2 + 23x + 15 ANSWER + 1, + 3, + 5 + 15 2. f (x) =2x 3 + 3x 2 – 11x – 6 1 + 1, + 2, + 3, + 6, +, 3 2 2 + ANSWER

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