Trying to factorize the following polynomial into irreducible polynomials in $\mathbb Z[x]$:
$$f(x) = 3x^3 + 2x^2 + 2x - 1.$$
So this factorizes into $(3x-1)(x^2 + x + 1)$ where $x^2 + x + 1$ is irreducible but I'm not sure what to do with $3x-1$.
Any help would be appreciated.