Question

How do you simplify and divide `(9d^3+5d-8)/(3d-2)`?

Answer 1

`3d^2+2d+3` with remainder`-2`

Explanation:

`color(white)(aaaaaaaaaaaa)` `3d^2+2d+3`
`color(white)(aaaaaaaaaaaa)` `-----`
`color(white)(aaaaa)3d-2` `|` `9d^3 +5d-8`
`color(white)(aaaaaaaaaaaa)` `9d^3-6d^2` `color(white)`
`color(white)(aaaaaaaaaa)` `----`
`color(white)(aaaaaaaaaaaaaa)` `0+6d^2+5d`
`color(white)(aaaaaaaaaaaaaaaaaa)` `6d^2-4d`
`color(white)(aaaaaaaaaaaaaaaaa)` `---`
`color(white)(aaaaaaaaaaaaaaaaaa)` `0+9d-8`
`color(white)(aaaaaaaaaaaaaaaaaaaa)` `+9d-6`
`color(white)(aaaaaaaaaaaaaaaaaaa)` `---`
`color(white)(aaaaaaaaaaaaaaaaaaaaaaa)` `0-2`

The remainder is `=-2` and the quotient is `=3d^2+2d+3`