Question 1
3 pts
Write the factored form of a cubic function in terms of $x$ that describes the volume of a box cut from a rectangular sheet of cardboard measuring 24 inches by 38 inches before the corners are removed.

The cuts allow the sides of the box to fold up around its base. The volume of a box is calculated by multiplying its length times width times height. $V=l \cdot w \cdot h$

Step 1 ：The problem involves a rectangular sheet of cardboard measuring 24 inches by 38 inches. Corners are cut from this sheet to form a box.

Step 2 ：The volume of a box is calculated by multiplying its length, width, and height. In this case, the length and width of the box are reduced by twice the height (since a square of side length \(h\) is cut from each corner of the cardboard), and the height of the box is \(h\).

Step 3 ：Therefore, the volume of the box can be expressed as a function of \(h\) as follows: \(V(h) = (24-2h)(38-2h)h\).

Step 4 ：Expanding this equation, we get the expanded form of the cubic function as \(V(h) = 4h^3 - 124h^2 + 912h\).

Step 5 ：\(\boxed{V(h) = 4h^3 - 124h^2 + 912h}\) is the final answer.