# Multiplying Polynomials

SportBounceCo makes and packages balls for different sports. Use your knowledge of polynomials to help the company design the box for one of its products.

Option 1: Volleyball

A volleyball is a sphere, so it's box will need to have a square base. SportsBounceCo makes volleyballs with three different diameters: 8 inches, 9 inches, and 10 inches. You will use what you know about polynomials to find out how much material you will need to make the boxes.

Option 2: Football

A football is twice as long as it is wide, so it's box will need to have a rectangular base. SportsBounceCo makes footballs in three lengths: 8 inches, 10 inches, and 12 inches. You will ise what you know about polynomials to find out how much material you will need to make the boxes.

1. Which ball did you select? What do you know about the base of the box? (2 points: 1 point for the selection, 1 point for the information)

• 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 will have a clear plastic top, so customers can see 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 the Tile Tool to help you draw and label the necessary dimensions for your cardboard sheet. Use x for the width and x + 1 for the height. (4 points: 2 points for the drawing, 2 points for correct labels)

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 points: 2 points for the product of binomials, 2 points for trinomial form)

4. Next write an equation for the surface area of the box (after the sheet has been folded). Don't include a top for the box; the top will be added later. (2 points: 2 points for the correct equation)

5. Fill in the table below to calculate the amount of material wasted in producing each size of box. Show your work. (6 points: 2 points for each different width)

 Ball Diameter Area of Full Sheet of Cardboard Surface Area of Box Area Removed from Corners 8 inches 9 inches 10 inches

 Ball Diameter Area of Full Sheet of Cardboard Surface Area of Box Area Removed from Corners 4 inches 5 inches 6 inches

A Fraction of a Problem

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? (2 points: 1 point for a correct response, 1 point for an explanation)

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1. The questioner was satisfied with and accepted the answer, or
2. The answer was evaluated as being 100% correct by the judge.

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