What is the complete factorization of the polynomial below

x^3-4x^2+x-4?

A. (x-4) (x+i) (x-1)

B. (x+4) (x+i) (x-i)

C. (x+4) (x-i) (x-i)

D. (x-4) (x-i) (x-i)

The answer to this question is D. (x-4) (x-i) (x-i).

x^3-4x^2+x-4 is divisible by (x-4) using Remainder theorem. Division leaves us with a quotient of x^2 + 1, which factors into (x-i) (x-i). Therefore all of the factors of (x-4) (x-i) (x-i).