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

Nov 28, 2017

The remainder is $0$ and the quotient is $= - {x}^{2} + 10 x - 25$

#### Explanation:

Let's perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$- 10$$|$$\textcolor{w h i t e}{a a a a}$$- 1$$\textcolor{w h i t e}{a a a a}$$0$$\textcolor{w h i t e}{a a a a a a}$$75$$\textcolor{w h i t e}{a a a a}$$- 250$

$\textcolor{w h i t e}{a a a a a a a a}$|color(white)(aaaa)color(white)(aaaaaa)10$\textcolor{w h i t e}{a a a}$$- 100$$\textcolor{w h i t e}{a a a a a}$$250$

$\textcolor{w h i t e}{a a a a a a a a a}$_________________________________________________________

$\textcolor{w h i t e}{a a a a a a a a}$|color(white)(aaaa)$- 1$$\textcolor{w h i t e}{a a a a}$$10$$\textcolor{w h i t e}{a a a a}$$- 25$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{red}{0}$

The remainder is $0$ and the quotient is $= - {x}^{2} + 10 x - 25$