A rectangular box has a square base. The combined length of a side of the square base, and the height is 20 in. Let x be the length of a side of the base of the box.

a. Write a polynomial function in factored form modeling the volume V of the box.
b. What is the maximum possible volume of the box?

a. V = (20-x)  

b . 1185.185

Step-by-step explanation:

Given that:

a. Write a polynomial function in factored form modeling the volume V of the box.

As we know that, this is a rectangular box has a square base so the Volume of it is:

V = h *

<=> V = (20-x)  

b. What is the maximum possible volume of the box?

To  maximum the volume of it, we need to use first derivative of the volume.

<=> dV / Dx = -3 + 40x

Let dV / Dx = 0, we have:

-3 + 40x  = 0

<=> x = 40/3

=>the height h = 20/3

So  the maximum possible volume of the box is:

V = 20/3 * 40/3 *40/3

= 1185.185