Question

The lengths of three sides of a trapezoid are shown below:

Side 1: 16z2 − 4z + 2

Side 2: −2z + 21 + 7z2

Side 3: 2 − 3z + 18z2

The perimeter of the trapezoid is 17z3 + 60z2 + 2z − 5.

Part A: What is the total length of sides 1, 2, and 3, of the trapezoid? (4 points)

Part B: What is the length of the fourth side of the trapezoid? (3 points)

Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (3 points)

Answer 1

The total length of sides 1, 2 and 3 of the trapezoid is given by:

`(16z^2-4z+2)+(-2z+21+7z^2)+(2-3z+18z^2)\\ \\ =16z^2+7z^2+18z^2-4z-2z-3z+2+21+2\\ \\ =41z^2-9z+25`