Solution
= Solution
Regard the <polynomial> as an element of $\mathbb C[x][y]$:
$$
x^3y^3+(x^2-1)y^2+(x^3-1)y+(1-x).
$$
The prime $x-1$ divides every nonleading coefficient, its square does not divide the constant coefficient, and it does not divide the leading coefficient $x^3$. Eisenstein's criterion proves irreducibility over $\mathbb C(x)[y]$; the <polynomial> is primitive in $\mathbb C[x][y]$, so Gauss's lemma proves irreducibility there.