# How do you use synthetic division to divide (5x^3+6x+8)div(x+2)?

Apr 1, 2017

The quotient is $= 5 {x}^{2} - 10 x + 26$ and the remainder is $= - 44$

#### Explanation:

Let $f \left(x\right) = 5 {x}^{3} + 6 x + 8$

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}$$5$$\textcolor{w h i t e}{a a a a}$$0$$\textcolor{w h i t e}{a a a \forall A a}$$6$$\textcolor{w h i t e}{a a A a a}$$8$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\textcolor{w h i t e}{a a a a}$color(white)(aaaaaaa)|$\textcolor{w h i t e}{a a a a}$color(white)(aaaa)-10$\textcolor{w h i t e}{a a a a a}$$20$$\textcolor{w h i t e}{a a a}$$- 52$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________
$\textcolor{w h i t e}{a a a a}$color(white)(aaaaaaa)|$\textcolor{w h i t e}{a a a a}$$5$$\textcolor{w h i t e}{a a a}$$- 10$$\textcolor{w h i t e}{a a a a a}$$26$$\textcolor{w h i t e}{a a a}$$\textcolor{red}{- 44}$

$f \left(x\right) = \left(x + 2\right) \left(5 {x}^{2} - 10 x + 26\right) - 44$