Question

How do you use synthetic division to divide `(-x^3+75x-250)div(x+10)`?

Answer 1

The remainder is `0` and the quotient is `=-x^2+10x-25`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `-10` `|` `color(white)(aaaa)` `-1` `color(white)(aaaa)` `0` `color(white)(aaaaaa)` `75` `color(white)(aaaa)` `-250`

`color(white)(aaaaaaaa)` ###|#`color(white)(aaaa)` ###color(white)(aaaaaa)#`10` `color(white)(aaa)` `-100` `color(white)(aaaaa)` `250`

`color(white)(aaaaaaaaa)` #`_________________________________________________________`#

`color(white)(aaaaaaaa)` ###|#`color(white)(aaaa)` `-1` `color(white)(aaaa)` `10` `color(white)(aaaa)` `-25` `color(white)(aaaaaa)` `color(red)(0)`

The remainder is `0` and the quotient is `=-x^2+10x-25`