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| 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, what are the teams? |
| _______________________________________________________________ |
| 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 sum of the polynomials. |
Find the difference and sum polynomials for each team:
3. Team A
_______________________________________________________________
4. Team B
_______________________________________________________________
Each team then used the sum and difference polynomials as the dimensions of a rectangle. Write an expression for each perimeter.
5.Team A's rectangle _______________________________________________________________
6.Team B's rectangle ______________________________________________________________
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