How to factorize $(x-2)^5+x-1$? This is a difficult problem.
How to factorize this?
$$(x-2)^5+x-1$$
we can't do any thing now and we should expand it first:
$$x^5-10x^4+40x^3-80x^2+81x-33$$
but I can't factorize it.

finally found how looking in my previous questions.
first substitute $n=x-2$ then
$$(x-2)^5+x-1=n^5+n+1$$
$$n^5+n+1=n^5-n^2+n^2+n+1=n^2(n^3-1)+n^2+n+1$$
$$=n^2(n-1)(n^2+n+1)+n^2+n+1$$
$$=(n^2+n+1)(n^3-n^2+1)$$
