Question

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

Answer 1

`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)`