Question

How do you use synthetic division to find x=-1 for `P(x)= x^3+2x^2-5x+6`?

Answer 1

The remainder is `=12` and the quotient is `=x^2+x-6`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `-1` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaaaa)` `2` `color(white)(aaaaaa)` `-5` `color(white)(aaaaa)` `6`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaa)` `-1` `color(white)(aaaaaa)` `-1` `color(white)(aaaaa)` `6`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaaaaa)` `1` `color(white)(aaaaaa)` `-6` `color(white)(aaaa)` `color(red)(12)`

The remainder is `=12` and the quotient is `=x^2+x-6`

`(x^3+2x^2-5x+6)/(x+1)=x^2+x-6+12/(x+1)`