# How do you divide (x^3+6x^2-30x+102)div(x+10) using synthetic division?

Oct 23, 2016

The result $\frac{{x}^{3} + 6 {x}^{2} - 30 x + 102}{x + 10} = \left({x}^{2} - 4 x + 10\right) + \frac{2}{x + 10}$

#### Explanation:

Let's do the division
${x}^{3} + 6 {x}^{2} - 30 x + 102$$\textcolor{w h i t e}{a a a a a}$∣x+10
${x}^{3} + 10 {x}^{2}$$\textcolor{w h i t e}{a a a a a a a a a a a a a a a}$∣x^2-4x+10
$0 - 4 {x}^{2} - 30 x$
$\textcolor{w h i t e}{a a}$$- 4 {x}^{2} - 40 x$
$\textcolor{w h i t e}{a a a a a}$$0 + 10 x + 102$
$\textcolor{w h i t e}{a a a a a a a a a}$$10 x + 100$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$0 + 2$

The remainder $= 2$

so the result is $\frac{{x}^{3} + 6 {x}^{2} - 30 x + 102}{x + 10} = \left({x}^{2} - 4 x + 10\right) + \frac{2}{x + 10}$