Question

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)

Answer 1

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

Explanation:

Answer 2

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

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-√(-1)^2)(x-4)`

We apply difference of two squares to get:

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