Let $F$ be a field with characteristic different from seven. Show that the polynomial $f(x,y)=7x-x^2y+2xy^3-x^3y^4+y^{100}\in F[x,y]$ is irreducible.
Is the polynomial as an element of $Z[x,y]$?
I did something,but I am not sure it is true..
Because $F$ is field $F[x,y]$ is UFD. x is irreducible in $F[x]$ and consider $f\in F[x][y]$ Then by Eisenstein's Criteria (choose p=x) f is irreducible.. Same thing for Z[x,y] Am I right?