Marvin wants to purchase a rectangular rug. It has an area represented by the expression 4x^2+64x+256. what is the length and width. also what do the factors in the factored expressions represent

Answer: the length and width are

(x + 8) and (x + 8)

Step-by-step explanation:

The rug has an area represented by the expression

Area = 4x² + 64x + 256.

The factors in the factored expressions represent the length and width of the rug.

Dividing the the equation by 4, it becomes

x² + 16x + 64 = 0

We would find two numbers such that their sum or difference is 16x and their product is 64x^2.

The two numbers are 8x and 8x. Therefore,

x² + 8x + 8x + 64 = 0

x (x + 8) + 8 (x + 8) = 0

The factors are

(x + 8) (x + 8)