# How do you divide (10x^4+5x^3+4x^2-9)div(x+1) using synthetic division?

Feb 24, 2017

The quotient is $= 10 {x}^{3} - 5 {x}^{2} + 9 x - 9$ and the remainder $= 0$

#### Explanation:

We perform a synthetic division

$\textcolor{w h i t e}{a a a a}$$- 1$$\textcolor{w h i t e}{a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$10$$\textcolor{w h i t e}{a a a a}$$5$$\textcolor{w h i t e}{a a a a a}$$4$$\textcolor{w h i t e}{a a a a a a}$$0$$\textcolor{w h i t e}{a a a a}$$- 9$

$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a a a}$$|$$\textcolor{w h i t e}{a a a}$$\textcolor{w h i t e}{a a a a}$$- 10$$\textcolor{w h i t e}{a a a a a}$$5$$\textcolor{w h i t e}{a a a a a}$$- 9$$\textcolor{w h i t e}{a a a a a}$$9$

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

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a a a a}$$10$$\textcolor{w h i t e}{a a a}$$- 5$$\textcolor{w h i t e}{a a a a a}$$9$$\textcolor{w h i t e}{a a a a a}$$- 9$$\textcolor{w h i t e}{a a a a a}$$\textcolor{red}{0}$

The remainder is $= 0$

The quotient is $= 10 {x}^{3} - 5 {x}^{2} + 9 x - 9$