Question

I need the answers to the question

Answer 1

Given

we have

$P(x)=x^3+2x^2+x+2$

Required

we need to write it in terms of linear factors.

Explanation

Here

$\begin{gathered} P(x)=x^3+2x^2+x+2 \\ =x^2(x+2)+x+2 \\ =(x+2)(x^2+1) \\ =(x+2)(x+i)(x-i) \\ so\text{ }P(x)=(x+2)(x+i)(x-i) \\ so\text{ }P(x)=(x+2)(x+\sqrt{-1})(x-\sqrt{-1}) \\ \end{gathered}$

the answer is (x+2)(x+i)(x-i)