Question

How do you divide `(m^3+6m^2+9m-5)div(m+1)` using synthetic division?

Answer 1

The remainder is `=-9` and the quotient is `=m^2+5m+4`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `-1` `color(white)(aaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaa)` `6` `color(white)(aaaa)` `9` `color(white)(aaaa)` `-5`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` ###color(white)(aaaaaaa)#`|` `color(white)(aaaa)` ###color(white)(aaa)#`-1` `color(white)(aa)` `-5` `color(white)(aaaa)` `-4`
`color(white)(aaaaaaaaaaaa)`________
`color(white)(aaaa)` ###color(white)(aaaaaaa)#`|` `color(white)(aaaa)` `1` `color(white)(aaaa)` `5` `color(white)(aaaa)` `4` `color(white)(aaaa)` `color(red)(-9)`

The remainder is `=-9` and the quotient is `=m^2+5m+4`