How do you divide #(2x^3 - 2x^2 -5x + 6)/(x-2)#?

1 Answer
Feb 15, 2017

#2x^2+2x-1+4/(x-2)#

Explanation:

One way is to express the numerator as factors of the divisor (x-2)

#color(red)(2x^2)(x-2)+(color(blue)(+4x^2)-2x^2)-5x+6#

#=color(red)(2x^2)(x-2)color(red)(+2x)(x-2)+(color(blue)(+4x)-5x)+6#

#=color(red)(2x^2)(x-2)color(red)(+2x)(x-2)color(red)(-1)(x-2)+(color(blue)(-2)+6)#

#rArr(2x^3-2x^2-5x+6)/(x-2)#

#=color(red)(2x^2+2x-1)+4/(x-2)#