Question

How do you divide `(x^3-x^2-14x+25)div(x-3)` using synthetic division?

Answer 1

The remainder is `=1` and the quotient is `=x^2+2x-8`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `3` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaaaa)` `-1` `color(white)(aaaaaa)` `-14` `color(white)(aaaaaaa)` `25`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaaaa)` `3` `color(white)(aaaaaaaa)` `6` `color(white)(aaaaa)` `-24`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaaaaa)` `2` `color(white)(aaaaaaa)` `-8` `color(white)(aaaaaaa)` `color(red)(1)`

`(x^3-x^2-14x+25)/(x-3)=(x^2+2x-8)+1/(x-3)`

The remainder is `=1` and the quotient is `=x^2+2x-8`