Question

How do you use long division to divide `(2x^3-4x^2-15x+5)/(x-1)^2`?

Answer 1

The answer is `=2x-((17x-5))/((x^2-2x+1))`

Explanation:

Let 's do the long division

`color(white)(aaaa)` `2x^3-4x^2-15x+5` `color(white)(aaaa)` `∣` `color(red)(x^2-2x+1)`

`color(white)(aaaa)` `2x^3-4x^2+2x` `color(white)(aaaaaaaaa)` `∣` `color(blue)(2x)`

`color(white)(aaaaaaa)` `0-0-17x+5`

Therefore,

`(2x^3-4x^2-15x+5)/(x^2-2x+1)=2x-((17x-5))/((x^2-2x+1))`