# How do you find the quotient of (4y^2+8y+3)div(y+2) using long division?

Mar 21, 2017

The remainder is $= 3$ and the quotient is $= 4 y$

#### Explanation:

We perform the long division

$\textcolor{w h i t e}{a a a a}$$4 {y}^{2} + 8 y + 3$$\textcolor{w h i t e}{a a a a}$$|$$y + 2$

$\textcolor{w h i t e}{a a a a}$$4 {y}^{2} + 8 y$$\textcolor{w h i t e}{a a a a a a a}$$|$$4 y$

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

The remainder is $= 3$ and the quotient is $= 4 y$

$\frac{4 {y}^{2} + 8 y + 3}{y + 2} = 4 y + \frac{3}{y + 2}$