# How do you divide (-3x^3 - x^2 - 11x + 30)/(2x+2)?

Apr 14, 2017

$- \frac{3}{2} {x}^{2} + x - \frac{13}{2} + \frac{43}{2 x + 2}$

#### Explanation:

What follows is the 'traditional long division' but in a different format. The processes are exactly the same.

$\text{ } - 3 {x}^{3} - {x}^{2} - 11 x + 30$
$\textcolor{m a \ge n t a}{- \frac{3}{2} {x}^{2}} \left(2 x + 2\right) \to \text{ "ul(-3x^3-3x^2) larr" subtract}$
$\text{ } 0 + 2 {x}^{2} - 11 x + 30$
$\text{ "color(magenta)(x)(2x+2)->" "ul(2x^2+2x) larr" subtract}$
$\text{ } 0 - 13 x + 30$
$\textcolor{w h i t e}{.} \textcolor{m a \ge n t a}{- \frac{13}{2}} \left(2 x + 2\right) \to \text{ } \underline{- 13 x - 13}$
$\textcolor{m a \ge n t a}{\text{ Remainder } \to 0 + 43}$

color(magenta)(-3/2x^2+x-13/2+43/(2x+2)