Show irreducible in k(x,y)[z]

Question

k is a field and $n\geq 1$. Show that $z^n+y^3+x^2 \in k(x,y)[z]$ is irreducible.

Can someone give hints? I am not sure how to apply Eisenstein's criterion to show irreducibility. Thank you

Answer 1

Eisenstein's criterion works, since $y^3+x^2$ is irreducible in $k[x,y]$, for degree reasons (y^3 can have no square root in $k[y]$).