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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?

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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.

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    It's considering $x,y$ primes in the polynomial ring $\mathbb{Q}[x,y]$? – 2017-01-23
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    More exactly, $y$ is prime in the P.I.D. $K[y]$ ($K$ any field). – 2017-01-23