Showing that $x^3 + 7x +2 $ is irreducible.

Question

I want to show that $f(x) = x^3 + 7x +2 \in \mathbb Z[x]$ is irreducible.

My idea is:

Let $a$ be a root of it then $2 = -a^3 - 7a$ then $a$ is a divisor of $2$ in $\mathbb Z$ therefore candidates for $a$ are $\pm 1, \pm 2.$ But then how can I complete? could someone clarify this to me please?