## How to go about proving that $-1+(x-4)(x-3)(x-2)(x-1)$ is irreducible in $\mathbb{Q}$?

How do you show that $-1+(x-4)(x-3)(x-2)(x-1)$ is irreducible in $\mathbb{Q}$? I don’t think you can use the eisenstein criterion here Answer Actually, the obvious generalization is also true. Let $P$ and $Q$ be polynomial factors, so that the given expression equals $PQ$. Then $PQ=-1$ at each of the integer values, $1,2,3,4$ for this case. So … Read more