I'm trying to prove this question:
Show that $p(x)=x^3 + ax^2 + bx +1 \in \mathbb Z [x]$ is reducible over $\mathbb Z$ if and only if either $a=b$ or $a+b=-2$.
I did the converse in this way:
if we take $a=b$, we see easily that $p(-1)=0$, so $p(x)$ has a root over $\mathbb Z$, then $p(x)$ is reducible over $\mathbb Z$.
I'm having problems with the first implication, I need some hints.