<s>[INST] Show that polynomial is reducible Show that $p(x)$ = $x^3 + 3x^2 + 2x + 4$ is reducible in $\mathbb{Z}$$/$$7$$\mathbb{Z}$
Is the approach for this to factor it and then find a root? I'm a little confused on how to start. Any tips appreciated.  
 [/INST] Another way:
\begin{align}p(x) &= x^3 + 3x^2 + 2x + 4\\
& = x^3 - 4x^2 + 2x + 4\\
& = x^3 - 2x^2 - 2x^2 + 4x - 2x + 4\\
& = x^2(x - 2) - 2x(x - 2) - 2(x - 2)\\
& = (x^2 - 2x - 2)(x - 2).
\end{align}
</s>