# How do you divide (x^2+20x+5) / (x-4)?

Mar 14, 2018

Quotient $\textcolor{g r e e n}{x + 24}$, Remainder $\textcolor{red}{\frac{101}{x - 4}}$

#### Explanation:

Let’s use synthetic division to find the quotient and remainder.

$\textcolor{w h i t e}{a a a a a a a a a a a} 0 \textcolor{w h i t e}{a a a a a} 1 \textcolor{w h i t e}{a a a a} 24$
 color(white)(aaa aaa aa ) ———————-
$\textcolor{w h i t e}{a a a} 4 \textcolor{w h i t e}{a a a} | \textcolor{w h i t e}{a a a} 1 \textcolor{w h i t e}{a a a a} 20 \textcolor{w h i t e}{a a a a} 5$
$\textcolor{w h i t e}{a a a a a a a} | \textcolor{w h i t e}{a a} \downarrow \textcolor{w h i t e}{a a a a} 4 \textcolor{w h i t e}{a a a a} 96$
 color(white)(aaa aaa a) | color(white)(aaa ) ——- ——-
$\textcolor{w h i t e}{a a a a a a a a a a a a} 1 \textcolor{w h i t e}{a a a a} 24 \textcolor{w h i t e}{a a a} 101$

Quotient $\textcolor{g r e e n}{x + 24}$, Remainder $\textcolor{red}{\frac{101}{x - 4}}$

Verification : $\left(x + 24\right) \cdot \left(x - 4\right) = {x}^{2} + 20 x - 94 + 101 = {x}^{2} + 20 x + 5$