math please help!!!!!

Factor f(x) into linear factors given that k is a zero of f(x).

f(x)=x^3+(12-4i)x^2+(32-48i)x-128i, k=4i
In completely factored form, f(x) =____
(factor completely. simplify your answer)

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asked by Ernie
  1. Since you are telling me that 4i = k
    then
    f(x)=x^3+(12-4i)x^2+(32-48i)x-128i
    =x^3 + (12 - k)x^2 + (32 - 12k) - 32k

    and since k is a zero, then (x - k) is a factor
    by synthetic division:
    f(x)=x^3+(12-4i)x^2+(32-48i)x-128i
    = (x-k)(x^2 + 12x + 32)
    = (x - 4i)(x^2 + 12x + 32)

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    posted by Reiny

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