Let $P$ $\in$ $\mathbb{F}_{p}[x,y]$, if $P$ does not have multiple factors then $P-1$ is irreducible.

Question

I need to show the following:

Let $P$ $\in \mathbb{F}_{p}[x,y]$. If $P$ does not have multiple factors, then $P-1$ is irreducible."

Please help.

Answer 1

For $p=3$ the polynomial $P:=x^2+1\in\Bbb{F}_3[x,y]$ does not have multiple factors, but $P-1=x^2$ is reducible. So the statement is false.