There's this following rewrite that I don't get. I have little to no experience with $o$'s and $\epsilon(x)s$ other than basic knowledge from a definition.
$$(o((x-a)^n) = \frac{1}{n!}\epsilon(x)(x-a)^n$$
I get the $\epsilon(x)(x-a)^n$ part from the definition of being little o of something, but where's the $\frac{1}{n!}$ coming from?