Prove that some bivariate polynomial is irreducible 
How can I prove that $p(x,y)=2xy+x^2+y^3$ is irreducible over the ring $\mathbb{R}[x,y]$? Is there, for instance, any way to generalize Eisenstein's criterion to polynomials in several variables?

I have tried a proof by contradiction without success, also I am looking for stronger techniques when it comes to polynomials in more than one variable. Any help? 

Hints :
For $y=2$ you have $p(x,2)=x^2+4x+8$ which is irreducible..
So.... Can you guess something??? 
