How do you divide ( x^3+3x^2+4x+12 )/(x^2+2x)?

Jun 30, 2018

The remainder is $= 2 x + 12$ and the quotient is $= x + 1$

Explanation:

Perform a long division

$\textcolor{w h i t e}{a a a a}$${x}^{3} + 3 {x}^{2} + 4 x + 12$$\textcolor{w h i t e}{a a a a}$$|$${x}^{2} + 2 x$

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

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

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

$\textcolor{w h i t e}{a a a a a a a a a}$$0 + 2 x + 12$

The remainder is $= 2 x + 12$ and the quotient is $= x + 1$

$\frac{{x}^{3} + 3 {x}^{2} + 4 x + 12}{{x}^{2} + 2 x} = \left(x + 1\right) + \frac{2 x + 12}{{x}^{2} + 2 x}$