Question

A company that manufactures and ships widgets has two different sizes for boxes. One size box has a volume modeled by the function f(x) = x^3 - 500x + 3000. The other size box has a volume modeled by the function g(x) = 4x^3 - 20x^2 - 240x. Write a simplified polynomial expression with terms in descending order that models the combined volume for one small box and one large box.

Answer 1

The combined volume for one small box and one large box is 5x^3 - 20x^2 - 740x + 3000.

Step-by-step explanation:

To find the combined volume for one small box and one large box, we need to add the volumes of the two boxes together. The volume of the small box is given by the function f(x) = x^3 - 500x + 3000, and the volume of the large box is given by the function g(x) = 4x^3 - 20x^2 - 240x. Adding the two volumes together, we get:

(x^3 - 500x + 3000) + (4x^3 - 20x^2 - 240x) = 5x^3 - 20x^2 - 740x + 3000

So, a simplified polynomial expression that models the combined volume for one small box and one large box is 5x^3 - 20x^2 - 740x + 3000.