# How do you divide (x^3-9x^2+27x-28)div(x-3) using synthetic division?

Jul 11, 2018

The remainder is $= \left(- 1\right)$ and the quotient is $= \left({x}^{2} - 6 x + 9\right)$

#### Explanation:

Let's perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$3$$|$$\textcolor{w h i t e}{a a a a}$$1$$\textcolor{w h i t e}{a a a a}$$- 9$$\textcolor{w h i t e}{a a a a a a}$$27$$\textcolor{w h i t e}{a a a a a}$$- 28$

$\textcolor{w h i t e}{a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a}$$3$$\textcolor{w h i t e}{a a a a a}$$- 18$$\textcolor{w h i t e}{a a a a a a}$$27$

$\textcolor{w h i t e}{a a a a a a a a a}$_________________________________________________________

$\textcolor{w h i t e}{a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$1$$\textcolor{w h i t e}{a a a a}$$- 6$$\textcolor{w h i t e}{a a a a a a a}$$9$$\textcolor{w h i t e}{a a a a a}$$\textcolor{red}{- 1}$

The remainder is $= \left(- 1\right)$ and the quotient is $= \left({x}^{2} - 6 x + 9\right)$

Therefore,

$\frac{{x}^{3} - 9 {x}^{2} + 27 x - 28}{x - 3} = {x}^{2} - 6 x + 9 - \frac{1}{x - 3}$