Actually you can use Eisenstien, but you need to fix it up first.

Gauss's lemma is the key that you need.

Let R be a Unique factorization domain with field of fractions F and let if p(x) is reducible in F[x] then p(x) is reducible in R[x].

What you actually want is the contraposative.

if p(x) is irreducible in R[x] then it is irreducable in F[x]

So in your case R is the integers and F is the rationals.

You should be able to finish from here

Happy hunting