# The area of a rectangular billboard is x^2+x-30 square meters. If the length is x + 6 meters, how do you find a binomial that represents the width?

Mar 1, 2016

$\left(x - 5\right)$ is the binomial representing width.

#### Explanation:

To find the width of a rectangular billboard whose area is $\left({x}^{2} + x - 30\right)$ square meters, If the length is $\left(x + 6\right)$ meters, one has to divide area by length.

Hence, width is $\frac{{x}^{2} + x - 30}{x + 6}$

Factorizing $\left({x}^{2} + x - 30\right)$, by splitting middle term into $6 x$ and $- 5 x$, we get

$\left({x}^{2} + 6 x - 5 x - 30\right)$ or

$x \left(x + 6\right) - 5 \left(x + 6\right)$ i.e. $\left(x + 6\right) \left(x - 5\right)$

Hence, width is $\left(x + 6\right) \frac{x - 5}{x + 6}$

or $\cancel{x + 6} \frac{x - 5}{\cancel{x + 6}}$

or $\left(x - 5\right)$ is the binomial representing width.