I want to prove that $t^4+xt^3+yt^2+xt+1$ is irreducible over $\mathbb{C}[x,y]$.
I know that $\mathbb{C}[x,y][t]$ is a UFD just as $\mathbb{C}[x,y]$ because the base ring is a field. Can I just change the order of the indeterminates and use $x$ as indeterminate to show that it is irreducible?