First, pull out a factor of 
.
Notice that when
(which you can arrive at via the rational root theorem), you have
which means you can pull out a factor of
. Upon dividing you get
The rational root theorem will come in handy again, suggesting that appears a second time as a root, which means
Now this is more readily factored without having to resort to the rational root theorem. You have
so in fact, shows up as a root for a third time.
So, you have
Two roots are obvious,
and (with multiplicity 3). The remaining two are given by
Notice that when
which means you can pull out a factor of
The rational root theorem will come in handy again, suggesting that
Now this is more readily factored without having to resort to the rational root theorem. You have
so in fact,
So, you have
Two roots are obvious,