Question

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?

Answer 1

`(x-5)` is the binomial representing width.

Explanation:

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

Hence, width is `(x^2+x-30)/(x+6)`

Factorizing `(x^2+x-30)`, by splitting middle term into `6x` and `-5x`, we get

`(x^2+6x-5x-30)` or

`x(x+6)-5(x+6)` i.e. `(x+6)(x-5)`

Hence, width is `(x+6)(x-5)/(x+6)`

or `cancel(x+6)(x-5)/cancel(x+6)`

or `(x-5)` is the binomial representing width.