In the ring $\displaystyle \mathbb{Z}[\sqrt{2}]$, determine can the following elements be decomposed into primary factors and is the decomposition unique:

$\displaystyle 5, 2+\sqrt{2}, 1+\sqrt{2}$.

I can't find anything in my notes on this, could someone please help me out, or maybe direct me to some online notes where it is explained?

Thank you!