Question

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

Answer 1

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)`