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 the box.

can some explain how to get the solution

Divide the volume by the height to get the area of the bottom. You don't say what the height is. You need to know it to do the problem.

the height is x+2

so the problem is
(x^2+5x+6)(x+5)+(x+2)
(x^2+10x^2+31x+30)+x+2
x^3+10^2+32x+30+2
x^3+10x^2+32x+32


Did I do this correct

Your expression factors into
(x+2)(x+3)(x+5)
where the individual factors would represent the width, length, and height of the box in no particular order.

So multiplying any two of the three could be the area of the bottom.
(x+2)(x+3) ---> x^2 + 5x + 6 or
(x+2)(x+5) ---> x^2 + 7x + 10 or
(x+3)(x+5) ---> x^2 + 8x + 15

(the box could be placed with any one of its 3 different faces at the bottom)



If the height is x+2....

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

Correct?

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

(x+3)(x+2)(x+3)/x+2 = (x+3)(x+3)

Is this correct?