# How do you divide (4x+2x^3+7x^2-1)div(x+1) using synthetic division?

Nov 5, 2016

The result is $2 {x}^{2} + 5 x - 1$

#### Explanation:

Let's do the long division
$\textcolor{w h i t e}{a a}$$2 {x}^{3} + 7 {x}^{2} + 4 x - 1$$\textcolor{w h i t e}{a a}$∣$x + 1$
$\textcolor{w h i t e}{a a}$$2 {x}^{3} + 2 {x}^{2}$$\textcolor{w h i t e}{a a a a a a a a a a}$∣$2 {x}^{2} + 5 x - 1$
$\textcolor{w h i t e}{a a a a}$$0 + 5 {x}^{2} + 4 x$
$\textcolor{w h i t e}{a a a a a a a a}$$5 {x}^{2} + 5 x$
$\textcolor{w h i t e}{a a a a a a a a a a}$$0 - x - 1$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$- x - 1$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$- 0 - 0$

$\frac{2 {x}^{3} + 7 {x}^{2} + 4 x - 1}{x + 1} = 2 {x}^{2} + 5 x - 1$