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

## I changed $\left(- {4}^{3}\right) \rightarrow \left(- 4 {x}^{3}\right)$. Sorry if this is not what was intended, but it seemed more likely.

Jul 5, 2016

$- 4 {x}^{2} - 13 x - 36 - \frac{112}{x - 3}$

#### Explanation:

$\text{ } - 4 {x}^{3} - {x}^{2} + 3 x - 4$
$\textcolor{m a \ge n t a}{- 4 {x}^{2}} \left(x - 3\right) \to \underline{- 4 {x}^{3} + 12 {x}^{2}} \leftarrow \text{ Subtract}$
$\text{ } \textcolor{w h i t e}{. .} 0 - 13 {x}^{2} + 3 x - 4$
$\textcolor{m a \ge n t a}{- 13 x} \left(x - 3\right) \to \text{ "ul(color(white)(..)-13x^2+39x)" "larr" Subtract}$
$\text{ } 0 \textcolor{w h i t e}{. .} - 36 x - 4$
$\textcolor{m a \ge n t a}{- 36} \left(x - 3\right) \to \text{ "color(white)(..)ul(-36x+108)" "larr" Subtract}$
" "0color(white)(..)color(magenta)(-112 larr" Remainder")

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$\textcolor{m a \ge n t a}{- 4 {x}^{2} - 13 x - 36 - \frac{112}{x - 3}}$