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)

Question

asked Jun 24, 2019 123k views

1 Answer

Jawnnypoo · Answer 1 · 2019-06-30T06:58:45+0000

Hello from MrBillDoesMath!

Answer: 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