# How do you find the quotient of (2x^3+7x^2-x+1)div(x+2) using synthetic division?

May 25, 2017

The quotient is $= 2 {x}^{2} + 3 x - 7$

#### Explanation:

Let's perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$- 2$$\textcolor{w h i t e}{a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$2$$\textcolor{w h i t e}{a a a a a a}$$7$$\textcolor{w h i t e}{a a a a a a}$$- 1$$\textcolor{w h i t e}{a a a a a}$$1$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$_________

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a}$$- 4$$\textcolor{w h i t e}{a a a a a a}$$- 6$$\textcolor{w h i t e}{a a a a}$$14$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$2$$\textcolor{w h i t e}{a a a a a a a}$$3$$\textcolor{w h i t e}{a a a a a a}$$- 7$$\textcolor{w h i t e}{a a a a}$$\textcolor{red}{15}$

$\frac{2 {x}^{3} + 7 {x}^{2} - x + 1}{x + 2} = \left(2 {x}^{2} + 3 x - 7\right) + \frac{15}{x + 2}$

The remainder is $= 15$ and the quotient is $= 2 {x}^{2} + 3 x - 7$