Question

How do you find the quotient `a^2+4a-22 div a-3` using long division?

Answer 1

The remainder is `=-1` and the quotient is `=a+7`

Explanation:

`color(white)(aaaaaaaaaa)` `a+7`
`color(white)(aaaaaaaaaa)` `-----`
`color(white)(aaaa)a-3` `|` `a^2+4a-22` #color(white) (aaaa)# `∣` `color(blue)(a+7)`

`color(white)(aaaaaaaaaa)` `a^2-3a` `color(white)`
`color(white)(aaaaaaaaaa)` `----`
`color(white)(aaaaaaaaaaaaa)` `0+7a-22`

`color(white)(aaaaaaaaaaaaaaaaa)` `7a-21`
`color(white)(aaaaaaaaaaaaaaaaa)` `---`
`color(white)(aaaaaaaaaaaaaaaaaa)` `0-1`

The remainder is `=-1` and the quotient is `=a+7`