we have that
(x^4 + 4x^3 – 5x^2 + x - 3)/ (x^2 + x -3)
x^2+3x-5
-x^4-x^3+3x^2
---------------------------------
3x^3-2x^2+x -3
-3x^3-3x^2+9x
-----------------------
-5x^2+10x -3
5x^2+5x -15
--------------------
15x-18
therefore
(x^4 + 4x^3 – 5x^2 + x - 3)=(x^2 + x -3)(x^2+3x-5)+(15x-18)
