Why is irreducible $x^{3n}+x^2y+xy^2+y$ in $\mathbb{Q}[x,y]$?

Question

I know how to prove that a polynomial is irreducible if it has one variable, but I don't know how to proceed with this problem:

Prove that for any positive integer $n$, the polynomial $x^{3n}+x^2y+xy^2+y$ is irreducible in $\mathbb{Q}[x,y]$.

Can anyone give me a hint or explain me how to solve it?

Answer 1

Eisenstein criterion in $\mathbf Q[y][x]$: $y$ divides all coefficients of the polynomial, but the leading coefficient, and $y^2$ doesn't divide its constant term.