# How do you find the quotient a^2+4a-22 div a-3 using long division?

Mar 16, 2017

The remainder is $= - 1$ and the quotient is $= a + 7$

#### Explanation:

$\textcolor{w h i t e}{a a a a a a a a a a}$$a + 7$
$\textcolor{w h i t e}{a a a a a a a a a a}$$- - - - -$
$\textcolor{w h i t e}{a a a a} a - 3$$|$${a}^{2} + 4 a - 22$color(white) (aaaa)∣$\textcolor{b l u e}{a + 7}$

$\textcolor{w h i t e}{a a a a a a a a a a}$${a}^{2} - 3 a$color(white)
$\textcolor{w h i t e}{a a a a a a a a a a}$$- - - -$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$0 + 7 a - 22$

$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$7 a - 21$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$- - -$
$\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 - 1$

The remainder is $= - 1$ and the quotient is $= a + 7$