Question

What is the complete factorization of the polynomial below

Answer 1

Answer:

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

Step-by-step explanation:

Let $P(x)=x^3-4x^2+x-4$

We can factor this polynomial by grouping:

$P(x)=x^2(x-4)+1(x-4)$

We factor further to obtain:

$P(x)=(x^2+1)(x-4)$

$P(x)=(x^2-\sqrt{-1}^2)(x-4)$

We apply difference of two squares to get:

$P(x)=(x-i)(x+i)(x-4)$

Answer 2

Answer:

(x+1)(x-1)(x+4)

Step-by-step explanation: