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)
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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