Question

The volume of a rectangular solid is modeled by a third degree polynomial function with zeros at 4,

3, and 0. If x is 2, then the volume of the box is 24 cubic units. Use this information to write the
polynomial that models the volume in standard form

Answer 1

The third degree polynomial function that models the volume of a rectangular solid with zeros at 4, 3, and 0 and a volume of 24 cubic units at x=2 is V(x) = 6x^3 - 42x^2 + 72x.

Step-by-step explanation:

The problem asks us to find the third degree polynomial function that models the volume of a rectangular solid with given zeros and a specific volume when x is 2.

First, we use the zeros to build the polynomial. Since the zeros are at 4, 3, and 0, the polynomial can be written in its factored form as V(x) = a(x - 4)(x - 3)(x - 0), where a is a constant.

To find the value of a, we substitute x = 2 and set V(2) = 24 cubic units, which gives us the equation 24 = a(2 - 4)(2 - 3)(2 - 0). Solving for a gives us a = 24/(-2)(-1)(2) = 6.

Therefore, the polynomial that models the volume in standard form is V(x) = 6(x - 4)(x - 3)(x - 0) or V(x) = 6x3 - 42x2 + 72x.