# How do you divide (y^4-8y^3+10y^2+2y+4)div(y-2) using synthetic division?

Jul 26, 2017

The remainder is $\textcolor{red}{0}$ and the quotient is $= {y}^{3} - 6 {y}^{2} - 2 y - 2$

#### Explanation:

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 a}$$|$$\textcolor{w h i t e}{a a}$$1$$\textcolor{w h i t e}{a a a a}$$- 8$$\textcolor{w h i t e}{a a a a a a}$$10$$\textcolor{w h i t e}{a a a a a a a}$$2$$\textcolor{w h i t e}{a a a a a a a}$$4$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$_________

$\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}$$2$$\textcolor{w h i t e}{a a a a}$$- 12$$\textcolor{w h i t e}{a a a a a}$$- 4$$\textcolor{w h i t e}{a a a a a a}$$- 4$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a a}$$|$$\textcolor{w h i t e}{a a a}$$1$$\textcolor{w h i t e}{a a a}$$- 6$$\textcolor{w h i t e}{a a a a a}$$- 2$$\textcolor{w h i t e}{a a a a a a}$$- 2$$\textcolor{w h i t e}{a a a a a a a}$$\textcolor{red}{0}$

The remainder is $\textcolor{red}{0}$ and the quotient is $= {y}^{3} - 6 {y}^{2} - 2 y - 2$

$\frac{{y}^{4} - 8 {y}^{3} + 10 {y}^{2} + 2 y + 4}{y - 2} = {y}^{3} - 6 {y}^{2} - 2 y - 2$