Irreducibility of the polynomial $(x-a)^n+p F(x)$ with $p$ prime

Question

Let $f(x)=(x-a)^n+pF(x)$ where $p$ is prime, $a\in\mathbb Z$ and $F(x)$ belongs to $\mathbb Z[x]$, $\deg(F)\leq n$ and $p$ does not divide $F(a)$. Then prove that $f(x)$ is irrreducible over $\mathbb Q[x]$.

Answer 1

Hint. Use Eisenstein criterion with the polynomial $f(x+a)$.