Question

How do you find the quotient of `(x^2-5x-16)div(x+2)`?

Answer 1

`x-7`

Explanation:

Using the following `color(blue)"algebraic manipulation"`

`"Using the divisor "(x+2)" as a factor in the numerator"`

`(x^2-5x-16)/(x+2)`

`=(color(red)(x)(x+2)+(color(blue)(-2x)-5x)-16)/(x+2)`

`=(color(red)(x)(x+2)color(red)(-7)(x+2)+(color(blue)(+14)-16))/(x+2)`

`=color(red)(x-7)-2/(x+2)`

`rArr"quotient "=x-7`

Answer 2

`x-7=quotient` and remainder `=-2`

Explanation:

`color(white)(aaaaaaaaaa)` `x-7`
`color(white)(aaaaaaaaaa)` `------`
`color(white)(aaaa)x+4` `|` `x^2-5x-16` #color(white) (aaaa)# `∣` `color(blue)`
`color(white)(aaaaaaaaaa)` `x^2+2x` `color(white)`
`color(white)(aaaaaaaaaa)` `----`
`color(white)(aaaaaaaaaaa)` `0-7x-16`
`color(white)(aaaaaaaaaaaaa)` `-7x-14`
`color(white)(aaaaaaaaaaaaaaaaa)` `---`
`color(white)(aaaaaaaaaaaaaaaaa)` `0-2`

remainder is `=-2` and the quotient is `=x-7`