Find an nth degree polynomial function satisfying the given conditions

Question

n=3

4 and 4i are zeros

f(1)=-102

Answer 1

c(x-4)(x+4i)(x-4i) = c(x-4)(x^2+16)

f(1) = -102

c(1-4)(1^2+16) = c(-3)(17) = -51c

-51c = -102

c = 2

Our polynomial is 2(x-4)(x^2+16)

We can multiply this out and get (2x-8)(x^2+16) =

2x^3 - 8x^2 + 32x - 128