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 box?can anyone show me how to do this?

Answer 1

This can be factored into
V = (x+2)(x+3)(x+5)
Sides are (x+2), (x+3) and (x+5)

Assuming that the box is closed:
Surface area = 2[(x+2)(x+3) + (x+2)(x+5) + (x+3)(x+5)]
= 2(x^2 + 5x + 6 + x^2 +7x + 10 + x^2 + 8x + 15)
= 2(3x^2 + 20x + 31)
= 6x^2 + 40x + 62

Answer 2

I think there is a problem with the way the question is stated. A box doesn't have an area. Each side has an area, however. So, maybe, the question is asking for the surface area of the box.

Now, to do that, let's factor the first polynomial. It breaks down to (x+3)(x+2).

So, the length of the sides of the box are (x+3), (x+2) and (x+5)

Now, the surface area is the area of each side multiplied by 2 since each side has an opposite with the same area.

So, you get:

2 *[(x+3)(x+2) + (x+3)(x+5) + (x+2)(x+5)] =
2 * (x^2 + 5x + 6 + x^2 + 8x + 15 + x^2 + 7x + 10) =
2 * (3x^2 + 20x + 31) =
6x^2 + 40x + 62

Answer 3

V = (x + 3)(x + 2)(x + 5)
The sides are (x + 3) , (x + 2) , (x + 5)
Surface Area
2 [(x + 2)(x + 3) + (x + 2)(x + 5) + (x + 3)(x + 5)]
2 [ x² + 5x + 6 + x² + 7x + 10 + x² + 8x + 15 ]
2 [ 3x² + 20x + 31 ]