# How do you use synthetic division to divide ( 6x^3 - 9x^2 - 12x - 6 ) / ( 3x + 4 )?

Dec 6, 2016

The quotient is $= 2 {x}^{2} - \frac{17}{3} x + \frac{32}{9}$ and the remainder is $= - \frac{182}{9}$

#### Explanation:

Let's do the division

$\textcolor{w h i t e}{a a a a}$$6 {x}^{3} - 9 {x}^{2} - 12 x - 6$$\textcolor{w h i t e}{a a a a}$∣$3 x + 4$

$\textcolor{w h i t e}{a a a a}$$6 {x}^{3} + 8 {x}^{2}$$\textcolor{w h i t e}{a a a a a a a a a a a a a}$∣$2 {x}^{2} - \frac{17}{3} x + \frac{32}{9}$

$\textcolor{w h i t e}{a a a a a}$$0 - 17 {x}^{2} - 12 x$

$\textcolor{w h i t e}{a a a a a a a}$$- 17 {x}^{2} - \frac{68}{3} x$

$\textcolor{w h i t e}{a a a a a a a a a a a}$$0 + \frac{32}{3} x - 6$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$+ \frac{32}{3} x + \frac{128}{9}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a a a}$$+ 0 - \frac{182}{9}$

The quotient is $= 2 {x}^{2} - \frac{17}{3} x + \frac{32}{9}$ and the remainder is $= - \frac{182}{9}$