# How do you divide (3x^4-2x^3+5x^2-4x-2)div(x+1) using synthetic division?

May 8, 2017

The remainder is $= 12$ and the quotient is $= 3 {x}^{3} - 5 {x}^{2} + 10 x - 14$

#### Explanation:

Let's perform the synthetic division

Let $f \left(x\right) = 3 {x}^{4} - 2 {x}^{3} + 5 {x}^{2} - 4 x - 2$

Let's perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$- 1$$\textcolor{w h i t e}{a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$3$$\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}$$5$$\textcolor{w h i t e}{a a a a a}$$- 4$$\textcolor{w h i t e}{a a a a a}$$- 2$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$_________

$\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 a}$$- 3$$\textcolor{w h i t e}{a a a a a a a}$$5$$\textcolor{w h i t e}{a a a a a}$$- 10$$\textcolor{w h i t e}{a a a a}$$14$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$3$$\textcolor{w h i t e}{a a a a a a}$$- 5$$\textcolor{w h i t e}{a a a a a a a}$$10$$\textcolor{w h i t e}{a a a a}$$- 14$$\textcolor{w h i t e}{a a a a a}$$\textcolor{red}{12}$

$f \left(x\right) = \left(3 {x}^{3} - 5 {x}^{2} + 10 x - 14\right) + \frac{12}{x + 1}$

The remainder is $= - 2$