Answer:
B. (x+4)(x+i)(x-i)
Step-by-step explanation:
Let [tex]P(x)=x^3-4x^2+x-4[/tex]
We can factor this polynomial by grouping:
[tex]P(x)=x^2(x-4)+1(x-4)[/tex]
We factor further to obtain:
[tex]P(x)=(x^2+1)(x-4)[/tex]
[tex]P(x)=(x^2-\sqrt{-1}^2)(x-4)[/tex]
We apply difference of two squares to get:
[tex]P(x)=(x-i)(x+i)(x-4)[/tex]
