# How do you find the quotient of (x^2+3x-28)div(x+7)?

Feb 9, 2017

See the entire solution process below:

#### Explanation:

First, rewrite the problem as:

$\frac{{x}^{2} + 3 x - 28}{x + 7}$

Next, factor the numerator:

$\frac{\left(x + 7\right) \left(x - 4\right)}{x + 7}$

Then, cancel the common terms in the numerator and denominator:

(color(red)(cancel(color(black)((x + 7))))(x - 4))/(color(red)(cancel(color(black)((x + 7))))

$x - 4$

However, because you cannot divide by $0$ we must qualify this answer:

$\left({x}^{2} + 3 x - 28\right) \div \left(x + 7\right) = \left(x - 4\right)$ where $x \ne - 7$