# How do you find the quotient of (b^3+3b-9)div(b+5) using long division?

Apr 30, 2017

The quotient is $= {b}^{2} - 5 b + 28$ and the remainder is $= - 131$

#### Explanation:

Let's perform the long division

$\textcolor{w h i t e}{a a a a}$${b}^{3}$$\textcolor{w h i t e}{a a a a a a}$$3 b - 9$$\textcolor{w h i t e}{a a a a}$$|$$b + 5$

$\textcolor{w h i t e}{a a a a}$${b}^{3} + 5 {b}^{2}$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a a a}$$|$${b}^{2} - 5 b + 28$

$\textcolor{w h i t e}{a a a a}$$0 - 5 {b}^{2} + 3 b$

$\textcolor{w h i t e}{a a a a a a}$$- 5 {b}^{2} - 25 b$

$\textcolor{w h i t e}{a a a a a a a a a a}$$0 + 28 b + 9$

$\textcolor{w h i t e}{a a a a a a a a a a a a}$$+ 28 b + 140$

$\textcolor{w h i t e}{a a a a a a a a a a a a a a a}$$0 - 131$

The quotient is $= {b}^{2} - 5 b + 28$ and the remainder is $= - 131$