# How do you divide (2x^3+9x^2+2x-21)div(x+3) using synthetic division?

Nov 15, 2016

The quotient is $= \left(2 {x}^{2} + 3 x - 7\right)$

#### Explanation:

Let's do the long division

$\textcolor{w h i t e}{a a a a}$$2 {x}^{3} + 9 {x}^{2} + 2 x - 21$$\textcolor{w h i t e}{a a a a}$∣$x + 3$

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

$\textcolor{w h i t e}{a a a a a a}$$0 + 3 {x}^{2} + 2 x$

$\textcolor{w h i t e}{a a a a a a a a}$$+ 3 {x}^{2} + 9 x$

$\textcolor{w h i t e}{a a a a a a a a a a a}$$0 - 7 x - 21$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$- 7 x - 21$

$\textcolor{w h i t e}{a a a a a a a a a a a a a a a}$$- 0 - 0$

The quotient is $= \left(2 {x}^{2} + 3 x - 7\right)$

no remainder