Question

How do you use long division to divide `(5x^2-17x-12)div(x-4)`?

Answer 1

`5x+3`

Explanation:

`color(white)(aaaaaaaaaa)` `5x+3`
`color(white)(aaaaaaaaaa)` `-----`
`color(white)(aaaa)x-4` `|` `5x^2-17x-12` #color(white) (aaaa)# `∣` `color(blue)(5x+3)`

`color(white)(aaaaaaaaaa)` `5x^2-20x` `color(white)`
`color(white)(aaaaaaaaaa)` `----`
`color(white)(aaaaaaaaaaaaa)` `0+3x-12`

`color(white)(aaaaaaaaaaaaaaaaa)` `3x-12`
`color(white)(aaaaaaaaaaaaaaaaa)` `---`
`color(white)(aaaaaaaaaaaaaaaaaa)` `0+0`

The remainder is `=0` and the quotient is `=5x+3`