Give $f(x)=a_0+a_1x+\ldots+a_nx^n$ and prime $p$ that $p \nmid a_n$ and $GCD(a_1,a_2,\ldots,a_n)=1$. Which one in two clause below is correct?
(1):"If $f(x)$ is irreducible in $\mathbb{Z}[x]$ then $f(x)$ is irreducible in $\mathbb{Z}_p[x]$.
(2):"If $f(x)$ is irreducible in $\mathbb{Z}_p[x]$ then $f(x)$ is irreducible in $\mathbb{Z}[x]$".
I have prove that (1) is wrong and i think (2) is correct but i can't prove it.