# How do you find the quotient (3y^3+8y^2+y-7)div(y+2) using long division?

##### 2 Answers
May 9, 2017

The quotient is $= 3 {y}^{2} + 2 y - 3$

#### Explanation:

Let's perform the long division

$\textcolor{w h i t e}{a a a a}$$3 {y}^{3} + 8 {y}^{2} + y - 7$$\textcolor{w h i t e}{a a a a}$$|$$y + 2$

$\textcolor{w h i t e}{a a a a}$$3 {y}^{3} + 6 {y}^{2}$$\textcolor{w h i t e}{a a a a a a a a a a a}$$|$$3 {y}^{2} + 2 y - 3$

$\textcolor{w h i t e}{a a a a a}$$0 + 2 {y}^{2} + y$

$\textcolor{w h i t e}{a a a a a a a}$$+ 2 {y}^{2} + 4 y$

$\textcolor{w h i t e}{a a a a a a a a}$$+ 0 - 3 y - 7$

$\textcolor{w h i t e}{a a a a a a a a a a a a}$$- 3 y - 6$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$- 0 - 1$

The quotient is $= 3 {y}^{2} + 2 y - 3$ and the remainder is $= - 1$

May 9, 2017

$3 {y}^{2} + 2 y - 3$