If x = 4i, x = 2, and x = -2, then your factors are (x - 4i), (x - 2), (x + 2), and also (x + 4i) because if 4i is a factor then -4i is as well.
[tex] f(x)=(x-4i)(x+4i)(x-2)(x+2)\\\\f(x)=(x^{2}-4xi+4xi+16)(x^{2}-2x+2x-4)\\\\f(x)=(x^{2}+16)(x^{2}-4)\\\\f(x)=x^{4}-4x^{2}+16x^{2}-64=x^{4} +12x^{2}-64 [/tex]
