Polynomial is irreducible over $\mathbb{Q}$ I've been scratching my head lately over this problem in my textbook:

Prove that the polynomial $x^4 + x^3 +x^2 +x +1$ is irreducible over $\mathbb{Q}$.

I've done some research and found this link, but they talk about Eisenstein's criterion, which we haven't covered in our math class just yet. Is there a general strategy where we can show whether a polynomial is irreducible over a field? 
My textbook really didn't go into depth on the topic of irreducibility of polynomials, but this Wiki link somewhat helps. Perhaps the rational root theorem may be helpful here, but how would I go about starting this proof?
EDIT
Please see the first comment for my initial strategy at showing the required result.

Note that in this case you can use Cohn's irreducibility criterion for base $b=2$, because $f(2)=31$ is a prime and the irreducibility follows.
