# How do you divide (3x^2 + x – 15) /(x – 3)?

Apr 9, 2018

#### Explanation:

The first step is to split the fraction into $2$ fractions where one is a multiple of the divisor and the second is the left over algebra. So

$\frac{3 {x}^{2} + x - 15}{x - 3}$

becomes

$\frac{3 {x}^{2} - 9 x}{x - 3} + \frac{10 x - 15}{x - 3}$

$= \frac{3 x \left(x - 3\right)}{x - 3} + \frac{10 x - 15}{x - 3}$
$= 3 x + \frac{10 x - 15}{x - 3}$

Repeating this process will divide the polynomial completely

$= 3 x + \frac{10 x - 30}{x - 3} + \frac{15}{x - 3}$

$= 3 x + \frac{10 \left(x - 3\right)}{x - 3} + \frac{15}{x - 3}$

$= 3 x + 10 + \frac{15}{x - 3}$

The process end here since the remaining fraction cannot be simplified further. And so:

$\frac{3 {x}^{2} + x - 15}{x - 3} = 3 x + 10 + \frac{15}{x - 3}$