# How do you divide (4x^3 + x^2 – 3x – 4)/((x + 8) )?

Apr 17, 2018

$4 {x}^{2} - 31 x + 245 - \frac{1964}{x + 8}$

#### Explanation:

Polynomial division is a lot like normal long division once you get the hang of it.

$\textcolor{w h i t e}{\frac{x + 8}{\textcolor{b l a c k}{x + 8}}} \textcolor{w h i t e}{x} \frac{4 {x}^{2} - 31 x + 245 \textcolor{w h i t e}{x} \textcolor{red}{- \frac{1964}{x + 8}}}{\text{)} \textcolor{w h i t e}{x} 4 {x}^{3} + \textcolor{w h i t e}{\times} {x}^{2} - \textcolor{w h i t e}{\times} 3 x - \textcolor{w h i t e}{x} 4}$
$\textcolor{w h i t e}{- X X X} \frac{- 4 {x}^{3} - \textcolor{w h i t e}{x} 32 {x}^{2} \textcolor{w h i t e}{\times \times}}{\textcolor{w h i t e}{\times \times x} - 31 {x}^{2} - \textcolor{w h i t e}{x} 3 x}$
$\textcolor{w h i t e}{- X X X X X X X} \frac{+ 31 {x}^{2} + 248 x \textcolor{w h i t e}{\times}}{\textcolor{w h i t e}{\times \times \times x} 245 x - 4}$
color(white)(- X X X X X X X X Xxxx) (-245x - 1960)/(color(white)(xxxxx) color(red)(-1964)

$- 1964$ is a remainder, so it gets put in a fraction over our divisor, $x + 8$.