Question

How do you long divide `( (t^3) - (6t^2) + (1) ) div (t +2)`?

Answer 1

`t^2-8t+16` and remainder`-31`

Explanation:

`color(white)(aaaaaaaaaa)` `color(blue)(t^2-8t+16`
`color(white)(aaaaaaaaaa)` `-----`
`color(white)(aaaa)t+2` `|` `t^3-6t^2+0+1` # #
`color(white)(aaaaaaaaaa)` `t^3+2t^2` `color(white)`
`color(white)(aaaaaaaaaa)` `----`
`color(white)(aaaaaaaaaa)` `0-8t^2+0`
`color(white)(aaaaaaaaaaaa)` `-8t^2-16t`
`color(white)(aaaaaaaaaaaaa)` `----`
`color(white)(aaaaaaaaaaaaaa)` `0+16t+1`
`color(white)(aaaaaaaaaaaaaaaaa)` `16t+32`
`color(white)(aaaaaaaaaaaaaaaaaaa)` `---`
`color(white)(aaaaaaaaaaaaaaaaaa)` `0-31`

The remainder is `color(blue)(=-31` and the quotient is `color(blue)(=t^2-8t+16`