Volume of a rectangular box is length × width × height. What expressions represent the length, width, and height of this box in terms of $x$?

Once you have a volume expression in terms of $x$, set it equal to $1{,}260$. Then think about how to rearrange that equation so it looks like the answer choices, which all have $0 =$ at the start.

In Desmos, create three expressions: h = x, L = 30 - 2x, and W = 24 - 2x to represent the height, length, and width of the box after cutting out squares of side $x$.

Type a new expression V(x) = h * L * W - 1260. This expression is zero exactly when the box volume is $1{,}260$ cubic inches.

Graph y = V(x) and look at its equation form on your screen. Compare that expression to the answer choices to see which one matches the model you just graphed.

When you cut out a square of side $x$ from each corner and fold up the sides:

• The height of the box becomes $x$ (the side length of the cut-out square).
• From the 30-inch side, you remove $x$ from each end, so the new length is $30 - 2x$.
• From the 24-inch side, you remove $x$ from each end, so the new width is $24 - 2x$.

Volume of a rectangular box is

Using the expressions we found:

• Length: $30 - 2x$
• Width: $24 - 2x$
• Height: $x$ So the volume in terms of $x$ is

We are told the volume is $1{,}260$ cubic inches, so we set the expression for volume equal to $1{,}260$:

This is the basic model of the situation in terms of $x$.

All answer choices are written with $0$ on one side. To match that form, subtract $1{,}260$ from both sides:

Rewriting with $0$ on the left, the correct model is

$0 = x(30 - 2x)(24 - 2x) - 1{,}260$.