How to factor polynomials? I am wondering if there is a methodical, algorithmic, brain-dead way to factor polynomials. For example:
$x^6 - 14x^{5} + 73x^{4} - 188x^{3} + 256x^{2} - 176x^{1} + 48$
can be written as
$(x-1)^2 (x-2)^3 (x-6)$
But how do you actually get there?

If you will accept a "brain-dead" method, why not just appeal to computer algebra, such as Mathematica?
Factor[x^6 - 14 x^5 + 73 x^4 - 188 x^3 + 256 x^2 - 176 x^1 + 48]

$(x-6) (x-2)^3 (x-1)^2$
or
Factor[-20284203008 + 12410729472 x + 2524112000 x^2 - 
  1341562640 x^3 - 334176180 x^4 + 12601652 x^5 + 12198347 x^6 + 
  1767405 x^7 + 127690 x^8 + 5150 x^9 + 111 x^10 + x^11]

$(x-4) (x-2)^2 (x+8)^3 (x+19)^5$
