we have
2x^5-x^4+3x^2-x+5 ÷ (x-1)
2x^4+x^3+x^2+4x+3
-2x^5+2x^4
----------------------------
x^4+3x^2-x+5
-x^4+x^3
--------------------
x^3+3x^2-x+5
-x^3+x^2
--------------------
4x^2-x+5
-4x^2+4x
---------------------
3x+5
-3x+3
------------
8 --------> remander
therefore
2x^5-x^4+3x^2-x+5 =(x-1)(2x^4+x^3+x^2+4x+3)+8
