# How do you find the quotient of (2s^3+3s^2-9s-10) div (s-2) using synthetic division?

May 20, 2017

The quotient is $= 2 {s}^{2} + 7 s + 5$

#### 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}$$3$$\textcolor{w h i t e}{a a a a a a}$$- 9$$\textcolor{w h i t e}{a a a a}$$- 10$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$_________

$\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 a}$$14$$\textcolor{w h i t e}{a a a a a}$$10$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\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$$\textcolor{w h i t e}{a a a a a}$$7$$\textcolor{w h i t e}{a a a a a a a a}$$5$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{red}{0}$

$\frac{2 {s}^{3} + 3 {s}^{2} - 9 s - 10}{s - 2} = \left(2 {s}^{2} + 7 s + 5\right)$

The remainder is $= 0$ and the quotient is $= 2 {s}^{2} + 7 s + 5$