# How do you divide (x^3+x^2-17x+15)div(x+5) using synthetic division?

Jul 20, 2017

The remainder is $0$ and the quotient is $= {x}^{2} - 4 x + 3$

#### Explanation:

Let's perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$- 5$$\textcolor{w h i t e}{a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$1$$\textcolor{w h i t e}{a a a a}$$1$$\textcolor{w h i t e}{a a a a a a}$$- 17$$\textcolor{w h i t e}{a a a a a a a}$$15$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$_________

$\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}$$- 5$$\textcolor{w h i t e}{a a a a a a a}$$20$$\textcolor{w h i t e}{a a a a a a}$$- 15$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a a}$$|$$\textcolor{w h i t e}{a a a}$$1$$\textcolor{w h i t e}{a a a}$$- 4$$\textcolor{w h i t e}{a a a a a a a a}$$3$$\textcolor{w h i t e}{a a a a a a a a}$$\textcolor{red}{0}$

The remainder is $\textcolor{red}{0}$ and the quotient is $= {x}^{2} - 4 x + 3$

$\frac{{x}^{3} + {x}^{2} - 17 x + 15}{x + 5} = {x}^{2} - 4 x + 3$