If P(4) = 0?

Question

If P(4) = 0, then a complete factorization of P(x) = 6x^3 – 34x^2 + 36x + 16 is

A) -2(x – 4)(x - 2)(3x + 1)
B) 2(x – 4)(x - 2)(3x + 1)
C) 2(x – 4)(x + 2)(3x - 1)
D) 2(x + 4)(x - 2)(3x + 1)

Answer 1

If P(4) = 0 then (x-4) is a factor, so we can rule out D. The coefficient of x^3 is positive, so we can rule out A. The remaining answers both have one negative and two positive roots, so we can't use the value of the constant term to distinguish between them; the easiest way is to see if P(2) = 0. Now P(2) = 6(8) - 34(4) + 36(2) + 16 = 48 - 136 + 72 + 16 = 0. So (x-2) is a factor, which means (B) must be the correct answer.

Answer 2

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