# How do you divide (3x^4+9x^3-2x^2+2x-7)/(x-2) ?

Jun 28, 2017

The remainder is $= 109$ and the quotient is $= 3 {x}^{3} + 15 {x}^{2} + 28 x + 58$

#### 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}$$|$$\textcolor{w h i t e}{a a a a}$$3$$\textcolor{w h i t e}{a a a a}$$9$$\textcolor{w h i t e}{a a a a a}$$- 2$$\textcolor{w h i t e}{a a a a}$$2$$\textcolor{w h i t e}{a a a a a}$$- 7$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$_________

$\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}$$6$$\textcolor{w h i t e}{a a a a a a}$$30$$\textcolor{w h i t e}{a a a}$$56$$\textcolor{w h i t e}{a a a a a}$$116$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$________

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a a}$$|$$\textcolor{w h i t e}{a a a}$$3$$\textcolor{w h i t e}{a a a}$$15$$\textcolor{w h i t e}{a a a a a}$$28$$\textcolor{w h i t e}{a a a}$$58$$\textcolor{w h i t e}{a a a a a}$$\textcolor{red}{109}$

The remainder is $= 109$ and the quotient is $= 3 {x}^{3} + 15 {x}^{2} + 28 x + 58$

Therefore,

$\frac{3 {x}^{4} + 9 {x}^{3} - 2 {x}^{2} + 2 x - 7}{x - 2} = 3 {x}^{3} + 15 {x}^{2} + 28 x + 58 + \frac{109}{x - 2}$