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

side 1: 4y + 2y2 − 3

side 2: −4 + 2y2 + 2y

side 3: 4y2 − 3 + 2y

the perimeter of the quadrilateral is 22y3 + 10y2 + 10y − 17.

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
i will give 40 points to the first correct answer!

  (A) 8y^2 +8y -10

  (B) 22y^3 +2y^2 +2y -7

  (C) yes, for these polynomials. The result of adding or subtracting the polynomials in this problem is another polynomial, suggesting the set of polynomials is closed to addition and subtraction.

Step-by-step explanation:

A. (4y + 2y^2 − 3) + (−4 + 2y^2 + 2y) + (4y^2 − 3 + 2y)

  = y^2(2 +2 +4) +y(4 +2 +2) +(-3 -4 -3)

  = 8y^2 +8y -10 . . . . total length of sides 1, 2, 3

__

B. The length of the 4th side is the difference between the perimeter and the sum of the other three sides:

  (22y^3 + 10y^2 + 10y − 17) -(8y^2 +8y -10)

  = 22y^3 +y^2(10 -8) +y(10 -8) +(-17 +10)

  = 22y^3 +2y^2 +2y -7 . . . . length of 4th side

__

C. The result of adding or subtracting the polynomials in this problem is another polynomial, suggesting the set of polynomials is closed to addition and subtraction. An example is not a proof, but there is nothing about this example that would suggest a different conclusion.