# How do you divide (x^2+2x-9) / (3x-4)  using polynomial long division?

Mar 19, 2016

Have a look at the method used in http://socratic.org/s/asSYFmWU
The values are different but the method is sound.

The solution for this question is: $\frac{x}{3} + \frac{10}{9} - \frac{41}{9 \left(3 x - 4\right)}$

#### Explanation:

Without breaking down the steps:

$\text{ } \frac{x}{3} + \frac{10}{9} - \frac{\textcolor{b l u e}{121}}{\textcolor{b l u e}{9} \textcolor{g r e e n}{\left(3 x - 4\right)}}$

" "color(green)(3x-4)" "|bar(" "color(brown)(x^2+2x-9))
$\text{ "|" "underline(x^2-(4x)/3 -)" Subtract}$
$\text{ "|" "0+(10x)/3 - 9" Bring down the 9}$
$\text{ "|" "underline((10x)/3-40/9 -)" Subtract}$
$\text{ "|" "0-color(blue)(41/9)" Remainder}$

Divide the remainder by $3 x - 4$ giving the last term of:

$- \frac{\textcolor{b l u e}{41}}{\textcolor{b l u e}{9} \textcolor{g r e e n}{\left(3 x - 4\right)}}$