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Published byAniyah Combs Modified about 1 year ago

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EXAMPLE 3 Use synthetic division Divide f (x)= 2x 3 + x 2 – 8x + 5 by x + 3 using synthetic division. –3 2 1 –8 5 –6 15 –21 2 –5 7 –16 2x 3 + x 2 – 8x + 5 x + 3 = 2x 2 – 5x + 7 – 16 x + 3 ANSWER SOLUTION

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EXAMPLE 4 Factor a polynomial Factor f (x) = 3x 3 – 4x 2 – 28x – 16 completely given that x + 2 is a factor. SOLUTION Because x + 2 is a factor of f (x), you know that f (–2) = 0. Use synthetic division to find the other factors. –2 3 –4 –28 –16 – –10 –8 0

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EXAMPLE 4 Factor a polynomial Use the result to write f (x) as a product of two factors and then factor completely. f (x) = 3x 3 – 4x 2 – 28x – 16 Write original polynomial. = (x + 2)(3x 2 – 10x – 8 ) Write as a product of two factors. = (x + 2)(3x + 2)(x – 4) Factor trinomial.

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GUIDED PRACTICE for Examples 3 and 4 Divide using synthetic division. 3. (x 3 + 4x 2 – x – 1) (x + 3) x 2 + x – x + 3 ANSWER 4. (4x 3 + x 2 – 3x + 7) (x – 1) 4x 2 + 5x x – 1 ANSWER

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GUIDED PRACTICE for Examples 3 and 4 Factor the polynomial completely given that x – 4 is a factor. 5. f (x) = x 3 – 6x 2 + 5x + 12 (x – 4)(x –3)(x + 1) 6. f (x) = x 3 – x 2 – 22x + 40 (x – 4)(x –2)(x +5) ANSWER

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