# How do you simplify and divide (9d^3+5d-8)/(3d-2)?

Feb 4, 2017

$3 {d}^{2} + 2 d + 3$ with remainder$- 2$

#### Explanation:

$\textcolor{w h i t e}{a a a a a a a a a a a a}$$3 {d}^{2} + 2 d + 3$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$- - - - -$
$\textcolor{w h i t e}{a a a a a} 3 d - 2$$|$$9 {d}^{3} + 5 d - 8$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$9 {d}^{3} - 6 {d}^{2}$color(white)
$\textcolor{w h i t e}{a a a a a a a a a a}$$- - - -$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a}$$0 + 6 {d}^{2} + 5 d$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a}$$6 {d}^{2} - 4 d$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$- - -$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a}$$0 + 9 d - 8$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a}$$+ 9 d - 6$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a}$$- - -$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a a a a}$$0 - 2$

The remainder is $= - 2$ and the quotient is $= 3 {d}^{2} + 2 d + 3$