Question

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

Side 1: 3y2 + 2y − 6

Side 2: 3y − 7 + 4y2

Side 3: −8 + 5y2 + 4y

The perimeter of the quadrilateral is 4y3 + 18y2 + 16y − 26.

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

Part B: What is the length of the fourth side of the quadrilateral? (4 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. (2 points)

Answer 1

In part A, we need to solve for the total length of sides 1, 2 and 3.
Since all three sides measurements are given, we have the solution below:
Sides123 = Side 1 + Side 2 + Side 3
Sides123 = (3y² + 2y - 6) + (4y² + 3y -7) + (5y² + 4y -8)
Sides123 = 12y² + 9y - 21
This is the total length of sides 1,2 and 3 "12y² + 9y - 21"

In part B, we need to solve for the length of the fourth side and the solution is shown below:
Side 4 = Perimeter / Sides123
Side 4 = (4y³ + 18y² + 16y -26) / 12y² + 9y -21