Problem
Show that $X^3-2008X^2+2010X-2009$ is irreducible in $\mathbb{Q}[X]$.
Progress
I considered applying Eisenstein's Theorem, but there are no primes $p$ such that $p|2008$, $p|2009$ and $p|2010$. (This is quite clear as $\nexists p$ prime such that p divides consecutive integers for any choice of p.)
I think this may require an application of Gauss's Lemma, but I'm yet to successfully show it. Any help would be appreciated.
Regards.