# How do you divide (x^3-6x^2-6x+9)div(x+1) using synthetic division?

Nov 12, 2016

The quotient is $= {x}^{2} - 7 x + 1$
The remainder is $= 8$

#### Explanation:

let's do the long division

$\textcolor{w h i t e}{a a a a}$${x}^{3} - 6 {x}^{2} - 6 x + 9$$\textcolor{w h i t e}{a a}$∣$x + 1$
$\textcolor{w h i t e}{a a a a}$${x}^{3} + {x}^{2}$$\textcolor{w h i t e}{a a a a a a a a a a a}$∣${x}^{2} - 7 x + 1$
$\textcolor{w h i t e}{a a a a a}$$0 - 7 {x}^{2} - 6 x$
$\textcolor{w h i t e}{a a a a a a a}$$- 7 {x}^{2} - 7 x$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$0 + x + 9$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$+ x + 1$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$+ 0 + 8$

So the quotient is $= {x}^{2} - 7 x + 1$

and the remainder $= 8$