<s>[INST] Factorize: $x^3 + x + 2$. How do I factorize the term $x^3 + x +2$?
What I have previously tried is the middle term factor method but it didn't work...
$x^3 + x + 2$
$\Rightarrow x^3 + 2x - x + 2$
$\Rightarrow x(x^2 + x) - 2(x - 1)$
This doesn't work.
What should I do?
 [/INST] Note
\begin{align}
x^3+x+2& = (x^3+x^2)-(x^2-x-2)\\
&= x^2(x+1)-(x-2)(x+1)\\
&=(x+1)(x^2-x+2)
\end{align}
</s>