What are the dimensions of the other two sides of a CD holder if the volume is V(x) = -x³ - x² + 6x?

To determine the dimensions of the other two sides of a CD holder when given the volume function ( V(x) = -x^3 - x^2 + 6x ), it's important to analyze the volume formula itself. Volume is typically calculated as the product of length, width, and height. In this case, if we assume that one of the dimensions is ( x ), then the goal is to express the volume in terms of ( x ) and deduce the remaining dimensions.

The given expression for volume can be factored or manipulated to find the dimensions more succinctly. First, we can factor ( V(x) ):

[

V(x) = -x^3 - x^2 + 6x = -x(x^2 + x - 6)

]

Next, we can factor the quadratic expression ( x^2 + x - 6 ) further:

[

x^2 + x - 6 = (x + 3)(x - 2)

]

Thus, we rewrite the volume function as:

[

V(x) = -x(x + 3)(x - 2)

]

This reveals that the volume is determined by the product involving the dimensions (