Is $\frac{p(x) - p(y)}{x-y}$ always irreducible?

Question

Let $p$ be an integer polynomial. Is $\frac{p(x) - p(y)}{x-y}$ always irreducible over the integers ?

Answer 1

Irreducibility is, in general, irreducibility over a field, but anyway, if we take $p(x)=x^4+x^2$ we have: $$ \frac{p(x)-p(y)}{x-y} = (x+y)\cdot(x^2+y^2+1).$$