Sometimes a good place to start is to guess the zero of the polynomial. For instance, if then . This tells us that is a factor.
Next, long divide (or use synthetic division) to reduce the degree of the polynomial. I leave it for you to show that
Also observe that if , then ; therefore, is a factor of . Apply long division again to get
Observe that cannot be factored nicely (it will involve square roots), so its best that we leave it like I did above.
Factoring in general is a game (to me anyways) and requires some intuition; there are a couple theorems out there that help make it a little easier (like the method I just used). Maybe you should take a look at those.
Does this make some sense?
EDIT: Take a look at this: http://tutorial.math.lamar.edu/Class...Factoring.aspx and see if this helps demystify the factoring process a little.