I'm very confused about how to prove the next statement. In class, we already know about the einsteins criterion and some tests of irreducibility but I don't remember any that taking into account the divisibility of the field characteristic. ( I rewrite the problem course I think it was badly redacted)
Statement: Let $k$ a field and $P(y) ∈ k[y]$ a polynomial which is not constant and not has repeated factors. Show that the polynomial $x^n - P(y)$ is irreducible in $k[x,y]$.
I don't really know even how to start so any help is welcome, Thank you in advance!
Attempt: I try by using Eisenstein's criterion to $x^n - P(y)$ as a polynomial with coefficients in $k[y]$ as a PID because remember that if F is a field then F[x] is a PID. But I really don't know how to use the criterion in a general case like P(y) like using the gcd? I don't get it.