(4x^3+2x^2-5)/2x-3 let's write this as
[4x^3 + 2x^2 + 0x - 5 ] / [2x - 3] now.....let's perform polynomial division
2x^2 + 4x + 6
2x - 3 [ 4x^3 + 2x^2 + 0x - 5 ]
4x^3 - 6x^2
------------------------------
8x^2 + 0x
8x^2 - 12x
-----------------
12x - 5
12x - 18
-----------
13
So our answer is : 2x^2 + 4x + 6 + 13 / [2x - 3]