Question

How do you long divide `(4x^3 - 6x^2 + 6) / (2x + 3)`?

Answer 1

The answer is `2x^2-6x+9-21/(2x+3`

Explanation:

Let's do the long division
`color(white)(aa)` `4x^3-6x^2` `color(white)(aaaaa)` `+6` `color(white)(aa)` `∣`2x+3
`color(white)(aa)` `4x^3+6x^2` `color(white)(aaaaaaaaaa)` `∣` `2x^2-6x+9`
`color(white)(aaa)` `0-12x^2`
`color(white)(aaaaa)` `-12x^2-18x`
`color(white)(aaaaaaaaa)` `0+18x+6`
`color(white)(aaaaaaaaaaa)` `+18x+27`
`color(white)(aaaaaaaaaaaaaaa)` `0-21`

`(4x^3-6x^2+6)/(2x+3)=2x^2-6x+9-21/(2x+3)`