Question

X^3 + 2x^2 + x + 2

Answer 1

If you're trying to factor, you can factor by grouping \(\Large \color{red}{(x^3+2x^2})+\color{green}{(x+2)}\)

Answer 2

(x + 1)(x + 1) = (x+1)^2 not equal to (x^2 + 1)
Further factoring will be with imaginary numbers. Maybe I am mistaken.

Answer 3

x^3+2x^2 +x +2=0 {You can solve this by factoring, or synthetic division. I will factor it}

Group Factor first two terms and second two terms--> Get the brackets to match.
x^2(x + 2) + 1(x + 2)

Combine the terms outside the brackets and multiply it by the common (x+2).
(x^2 + 1) (x + 2)