# How do you use synthetic division to divide (9x^3-16x-18x^2+32)div(x-2)?

Apr 2, 2017

The quotient is $= 9 {x}^{2} - 16$ and the remainder is $= 0$

#### Explanation:

Let $f \left(x\right) = 9 {x}^{3} - 18 {x}^{2} - 16 x + 32$

Let's perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$2$$\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}$$- 18$$\textcolor{w h i t e}{a a a}$$- 16$$\textcolor{w h i t e}{a a a a a}$$32$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$_________

$\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}$$18$$\textcolor{w h i t e}{a a a a a}$$0$$\textcolor{w h i t e}{a a a a}$$- 32$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\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$$\textcolor{w h i t e}{a a a a a a}$$0$$\textcolor{w h i t e}{a a a}$$- 16$$\textcolor{w h i t e}{a a a a a}$$\textcolor{red}{0}$

$f \left(x\right) = \left(x - 2\right) \left(9 {x}^{2} - 16\right) + 0$