What is the complete factorization of the polynomial below? x^3+4x^2+16x+64 a. (x-4)(x+4i)(x+4i) b. (x-4)(x+4i)(x-4i) c. (x+4)(x+4i)(x+4i) d. (x+4)(x+4i)(x-4i)

Hello from MrBillDoesMath!

 Choice D.  (x+4) ( x-4i)(x+4i)

Discussion:

Factor the polynomial:

x^3+4x^2+16x+64 =  (x +4 ) ( x^2 + 16)     (*)

Factor x^2 +1 6 over the complex numbers:

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

Combing (*) and (**) gives the full factorization

(x+4) ( x-4i)(x+4i)

which is choice B\D

Thank you,

MrB