A dentist's office and parking lot are on a rectangular piece of land.
The area (in square meters) of the land is represented by $x^{2} + x - 30$ .
Write a binomial that represents the width of the land.

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Solution

Step-1: Write the information given in the question:
The area of a rectangular piece of land is obtained by multiplying the length and width of the rectangle.
The area (in square meters) of the land is represented by $x^{2} + x - 30$ .
Step-2: Simplify the given equation.
Factorize the given equation.
$\begin{array}{rcl} x^{2} + x - 30 & = & x^{2} + 6 x - 5 x - 30 \\ \Rightarrow & = x (x + 6) - 5 (x + 6) \\ ∴ & = & (x + 6) (x - 5) \end{array}$
Hence, the width of the rectangle is either $(x + 6)$ or $(x - 5) .$

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A dentist's office and parking lot are on a rectangular piece of land. The area (in square meters) of the land is represented by x2+x-30. Write a binomial that represents the width of the land.

A dentist's office and parking lot are on a rectangular piece of land.
The area (in square meters) of the land is represented by $x^{2} + x - 30$ .
Write a binomial that represents the width of the land.