Show that there are infinitely many irreducible polynomials in $\Bbb Z\_2[x]$.

I have a strategy about how to do this but I need some help finding a contradiction. I want to assume there are finitely many irreducible polynomials. $p\_1,...p\_n$. Then I want to consider the irreducible factors of $(p\_1p\_2...p\_n)+1$. I don't really know where to go from here. Any help would be appreciated.