Question 1 (essay worth 10 points) (07.02 mc)
the lengths of three sides of a trapezoid are shown below: side 1: 11z2 + 4z − 6 side 2: 4z − 7 + 12z2 side 3: −8 + 13z2 + 4z the perimeter of the trapezoid is 7z3 + 42z2 − 15z + 1.

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)

Part A:
Side 1 + side 2 + side 3 = 11z2 + 4z − 6 + 4z − 7 + 12z2  −8 + 13z2 + 4z
                                       = 11z2 + 12z2 + 13z2 + 4z + 4z + 4z - 6 - 7 - 8
                                       = 36z2 + 12z -21

Part B:
The parameter of the trapezoid is the summation of the lengths of its four sides, thus:
Side 4 = Parameter - (side 1 + side 2 + side 3)
           = Parameter - output of part A
           = 7z3 + 42z2 − 15z + 1 - 36z2 - 12z + 21
           = 7z3 + 6z2 - 27z +22

Part C:
For a polynomial to be closed under addition and subtraction operations, the performance of these operations on the polynomial should give a new polynomial.
Since the addition in Part A and the subtraction in Part B both resulted in new polynomials, thus, the answers of these two parts show that polynomials are closed under addition and subtraction.

What’s the equation you are trying to solve to get x?

She should use 12/3 to measure