What is the fastest way to factor polynomials algebraically? What is the fastest way that you can do by hand? For example: (just a simple example, the answer should be general of course)

$x^4 -4x^3 +8x$

or 

$2x^2+3x+1$
Read up on Horner's Method. Ignore this part of the sentence as I just need to fill up the characters.
Read up on Horner's Method. Ignore this part of the sentence as I just need to fill up the characters.