1. thomas buys a cardboard sheet that is 8 by 12 inches. let x be the side length of each cutout. create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.
2. what is the size of the cutout he needs to make so that he can fit the most marbles in the box?
3. if thomas wants a volume of 12 in3, what size does the cutout need to be? what would be the dimensions of this box?
4. design an equation for the volume of a box made from a cardboard sheet of length q and width p and square cutouts of side length x.