Question

A rug has an area of ​x2+x−20 square feet. Which expression represents the dimensions of the rug? A ​(x+4)(x−5) B ​(x+2)(x−10) C ​(x−4)(x+5) D ​(x−2)(x+10)

Answer 1

Answer: the correct option is

C ​(x−4)(x+5)

Explanation:

The area of the rug in square feet is expressed as

​x^2+x−20

The given equation is a quadratic equation and the roots of the equation represents the dimensions of the rug. To simplify the equation, we would apply the factorization method.

We will get two numbers such that, their difference will be x and their sum will be -20x^2. The numbers are 5x and 4x. Therefore

​x^2+ 5x - 4x −20 = 0

x(x + 5) - 4(x +5)

The roots are (x - 4)(x + 5)