Use your knowledge of polynomials to help the company design the box for one of its products. I selected the football: It is twice as long as it is wide, so its box will have a rectangular base. SportsBounceCo makes volleyballs with three different diameters: 8 inches, 10 inches, and 12 inches. You will use what you know about polynomials to find out how much material you will need to make the boxes.
2. Here is some more information about making the boxes:
SportsBounceCo uses flat sheets of cardboard to make boxes.
The company uses square sheets for volleyball boxes and rectangular sheets for football boxes.
The boxes have no top, so that customers can see and touch the product.
The height of the box is always 1 inch greater than the width of the ball.
To assemble the box, corners are cut out of each sheet and the edges are taped together.
Use x for the width and x + 1 for the height.
3. Now use your drawing to write an equation for the area of the entire sheet of cardboard. First write the equation as the product of two binomials, and then as a simplified trinomial.
4. Next write an equation for the surface area of the box (after the sheet has been folded).
6. SportsBounceCo makes only boxes that have sides that are measured in whole inches, like the boxes you have been describing so far. Is it possible for them to produce a box that has a surface area that is not a whole number? How do you know?