How do you divide #(4x^3-8x^2+15x-16)/(2x-3)#?

1 Answer
Nov 1, 2016

The answer is #=2x^2-x+6+2/(2x-3)#

Explanation:

We do a long division
#color(white)(aaa)##4x^3-8x^2+15x-16##color(white)(aaa)##∣##2x-3#
#color(white)(aaa)##4x^3-6x^2##color(white)(aaaaaaaaaaaaa)##∣##2x^2-x+6#
#color(white)(aaaaa)##0-2x^2+15x#
#color(white)(aaaaaaa)##-2x^2+3x#
#color(white)(aaaaaaaaaa)##0+12x-16#
#color(white)(aaaaaaaaaaaaaa)##12x-18#
#color(white)(aaaaaaaaaaaaaaaa)##0+2#

So we have #(4x^3-8x^2+15x-16)/(2x-3)=2x^2-x+6+2/(2x-3)#