How do you divide (9x^3-19x^2-28x+12)div(x-3) using synthetic division?

May 21, 2017

The remainder is $= 0$ and the quotient is $= 9 {x}^{2} + 8 x - 4$

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}$$9$$\textcolor{w h i t e}{a a a a a a}$$- 19$$\textcolor{w h i t e}{a a a a a a}$$- 28$$\textcolor{w h i t e}{a a a a}$$12$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$_________

$\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}$$27$$\textcolor{w h i t e}{a a a a a a a}$$24$$\textcolor{w h i t e}{a a a}$$- 12$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$9$$\textcolor{w h i t e}{a a a a a a a a}$$8$$\textcolor{w h i t e}{a a a a a a}$$- 4$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{red}{0}$

$\frac{9 {x}^{3} - 19 {x}^{2} - 28 x + 12}{x - 3} = \left(9 {x}^{2} + 8 x - 4\right)$

The remainder is $= 0$ and the quotient is $= 9 {x}^{2} + 8 x - 4$