The volume of the box is represented by (x^2+5x+6)(x+5).?

Question

The volume of the box is represented by (x^2+5x+6)(x+5).Find
the polynomial that represents the area of the bottom of a cube

Answer 1

(x^2+5x+6) = (x+2)(x+3).

I'm assuming that the side lengths are x+2, x+3 and x+5.

However, how do I know which sides represent the length, width, and height? That is not specified.

Therefore, there are 3 possible answers:
(x+2)(x+3) = x^2 + 5x + 6
(x+2)(x+5) = x^2 + 7x + 10
(x+3)(x+5) = x^2 + 8x + 15

Answer 2

Well, the volume of a cube = L^3 and the area of a side = L^2

Say:

L^3 = (x^2+5x+6)(x+5)
L^3 = (x^3 + 10x^2 +31x + 30)
L^2 = (x^3 + 10x^2 +31x + 30)^(2/3)

A= L^2 =(x^3 + 10x^2 +31x + 30)^(2/3)