Modeling with polynomials: Volume of a rectangular box?

edit: The white part highlighted (before folding the box) is actually the top part of the box (not the bottom like I highlighted), but hopefully you get it (opposite sides of a rectangle are equal in length)

Here we use a third degree polynomial to model and analyze the volume of a rectangular box. we skipped the last question but feel free to try it. To my students- this video should be enough to finish the other questions in the slides (please try them!)

other topics mentioned: roots, volume, rectangular prism, functions, restricted domain, net