I stumbled upon this kind of problem and I really can't get the hang of it. Will anyone please outline the way to solve it?
Determine for which of the first $p > 0$ values the polynomial $f = 42x^4+21x^3-x+1 \in \mathbb Z_p$ is monic and has degree 3. Then factor it as product of irreducibile polynomials in the polynomial rings found.