# How do you divide ( -3x^3+ x^2-3x-28 )/(x + 1 )?

May 21, 2017

The quotient is $= - 3 {x}^{2} + 4 x - 7$ and the remainder is $= - 21$

#### Explanation:

Let's perform the long division

$\textcolor{w h i t e}{a a a a}$$x + 1$$|$$- 3 {x}^{3} + {x}^{2} - 3 x - 28$$\textcolor{w h i t e}{a a a a}$$|$$- 3 {x}^{2} + 4 x - 7$

$\textcolor{w h i t e}{a a a a a a a a a a}$$- 3 {x}^{3} - 3 {x}^{2}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$0 + 4 {x}^{2} - 3 x$

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

$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$+ 0 - 7 x - 28$

$\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}$$- 7 x - 7$

$\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}$$- 0 - 21$

The quotient is $= - 3 {x}^{2} + 4 x - 7$ and the remainder is $= - 21$