This activity was developed by students at Mainland High School in Daytona Beach, FL, over the summers 1998-1999/ Permission was given by the publishers to adapt the activty to html.
| Long-Term Project |
| Four contestants were selected for the new game show called
"Polynomial Permutations and Calculations." Use what you know about polynomials
to follow the contestants through each round and determine who won. In Round 1, each
contestant drew a number out of a hat, with the numbers ranging from 1 to 4. Each number
corresponded to a polynomial. The table shows the names of the contestants, the number
drawn, and the associated polynomial.
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1. Complete the table
| Name | Number | Polynomial |
Standard Form | Number of Terms | Degree |
| Fred | 1 | x 4 + 4x2 + 3 x7 | |||
| Sarah | 2 | x 4 + 8x6 + x + 5x7-x5 | |||
| Chuck | 3 | 4 + x3 + 4x4 + 2x2 + 9x | |||
| Jeannie | 4 | 5x - 11x2 + 3x3 + 5x5 + 3 |
| 2. If the contestant with the lowest degree polynomial is paired with the one with the highest degree polynomial to form Team A, and the two remaining contestants are paired to form Team B, who is on which team? |
| Next, both teams were asked to form two new polynomials: one being the difference between the higher order polynomial and the lower order polynomial of the team members, and the other being the sumof the polynomials. |
Find the difference and sum polynomials for:
3. Team A
4. Team B
Each team then use the sum and difference of their polynomials as the dimensions of a rectangle. Write an expression for each perimeter.
5. Team A's rectangle
6. Team B's rectangle
Each member of the team that had the rectangle with the larger perimeter when the value of x = 1 received 20 points. Find the value of each perimeter.
7. Team A? 8. Team B? 9. Which contestants received 20 points each? |
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Copyright 1997-1999: html adaptation
Career Connection to Teaching with Technology