Use the factor theorem to determine whether the binomial x-3 is a factor of the polynomial function f (x) = - 5x^3 + 16x^2 - 9

Question

Mathematics

Rigoberto Vargas

17 July, 05:51

Use the factor theorem to determine whether the binomial x-3 is a factor of the polynomial function f (x) = - 5x^3 + 16x^2 - 9

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Answers (1)

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Oswaldo Tapia · Answer 1

(x - 3) is a factor of f (x)

Step-by-step explanation:

If (x - h) is a factor of f (x) then f (h) = 0 ← factor theorem

Thus if (x - 3) is a factor of f (x) then f (3) = 0

f (3) = - 5 (3) ³ + 16 (3) ² - 9 = - 135 + 144 - 9 - 0

Thus (x - 3) is a factor of f (x)