Question

How do you find the quotient of `(2x^3+7x^2-x+1)div(x+2)` using synthetic division?

Answer 1

The quotient is `=2x^2+3x-7`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `-2` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `2` `color(white)(aaaaaa)` `7` `color(white)(aaaaaa)` `-1` `color(white)(aaaaa)` `1`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaa)` `-4` `color(white)(aaaaaa)` `-6` `color(white)(aaaa)` `14`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `2` `color(white)(aaaaaaa)` `3` `color(white)(aaaaaa)` `-7` `color(white)(aaaa)` `color(red)(15)`

`(2x^3+7x^2-x+1)/(x+2)=(2x^2+3x-7)+15/(x+2)`

The remainder is `=15` and the quotient is `=2x^2+3x-7`