Question

The lengths of three sides of a trapezoid are shown below:
Side 1: 11z2 − 4z + 2

Side 2: −2z + 3 + 12z2

Side 3: 3 − 3z + 13z2

The perimeter of the trapezoid is 5z3 + 40z2 + 7z − 15.

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

Part B: What is the length of the fourth side of the trapezoid?

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

I think I can help, but only with the first two sections (sorry!).

A: (11z^2-4z+2)+(12z^2-2z+3)+(13z^2-3z+3)
(11z^2+12z^2+13z^2)+(-4z+-2z+-3z)+(2+3+3)
A: 36z^2-9z+8

B: (5z^3+40z^2+7z-15)-(36z^2-9z+8)
5z^3+(40z^2-36z^2)+(7z+9z)+(-15-8)
B: 5z^3+4z^2+16z-23

Answer 2

Answer:

Part A: 11z^2 − 4z + 2 −2z + 3 + 12z^2-  3 − 3z + 13z2= (36z^2-9z+8)

Part B:  5z^3 + 40z^2 + 7z − 15-(36z^2-9z+8)

Part C: The answers show that the polynomials for Part A and B are closed under addition and subtraction. We can see that when we add both polynomials they result in a polynomial same applies to subtraction.