# How do you divide (x^3-x^2-14x+25)div(x-3) using synthetic division?

May 19, 2017

The remainder is $= 1$ and the quotient is $= {x}^{2} + 2 x - 8$

#### Explanation:

Let's perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$3$$\textcolor{w h i t e}{a 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 a a}$$- 1$$\textcolor{w h i t e}{a a a a a a}$$- 14$$\textcolor{w h i t e}{a a a a a a a}$$25$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$_________

$\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 a a}$$3$$\textcolor{w h i t e}{a a a a a a a a}$$6$$\textcolor{w h i t e}{a a a a a}$$- 24$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$1$$\textcolor{w h i t e}{a a a a a a a}$$2$$\textcolor{w h i t e}{a a a a a a a}$$- 8$$\textcolor{w h i t e}{a a a a a a a}$$\textcolor{red}{1}$

$\frac{{x}^{3} - {x}^{2} - 14 x + 25}{x - 3} = \left({x}^{2} + 2 x - 8\right) + \frac{1}{x - 3}$

The remainder is $= 1$ and the quotient is $= {x}^{2} + 2 x - 8$