# How do you use synthetic division to divide (3x^3 - 17x^2 + 15x - 25) -: (x-5)?

Jan 12, 2017

$3 {x}^{2} - 2 x + 5$

#### Explanation:

$\textcolor{w h i t e}{a a a a}$$3 {x}^{3} - 17 {x}^{2} = 15 x - 25$$\textcolor{w h i t e}{a a a a}$∣$\textcolor{g r e e n}{x - 5}$

$\textcolor{w h i t e}{a a a a}$$2 {x}^{3} - 15 {x}^{2}$color(white)(aaaaaaaaaaaaaa ∣$\textcolor{red}{3 {x}^{2} - 2 x + 5}$
$\textcolor{w h i t e}{a a a a a}$$- - - - -$

$\textcolor{w h i t e}{a a a a a a a}$$0 - 2 {x}^{2} + 15 x$

$\textcolor{w h i t e}{a a a a a a a a a}$$+ 2 {x}^{2} + 10 x$
$\textcolor{w h i t e}{a a a a a a a a a}$$- - - - -$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$0 - 5 x - 25$

$\textcolor{w h i t e}{a a a a a a a a a a a a a a a}$$- 5 x - 25$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a}$$- - - - -$

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

The remainder is $= 0$ and the quotient is $= 3 {x}^{2} - 2 x + 5$

$\frac{3 {x}^{3} - 17 {x}^{2} + 15 x - 25}{x - 5} = 3 {x}^{2} - 2 x + 5$

$\textcolor{w h i t e}{a a a a}$$3 {x}^{3} - 17 {x}^{2} + 15 x - 25$$\textcolor{w h i t e}{a a a a}$∣$\textcolor{g r e e n}{x - 5}$
$\textcolor{w h i t e}{a a a a}$$x - 5$$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a}$∣$\textcolor{red}{3 {x}^{2} - 2 x + 5}$
$\textcolor{w h i t e}{a a a a a a a a}$$- - - - -$