Question

The lengths of three sides of a quadrilateral are shown below: Side 1: 1y2 + 3y − 6 Side 2: 4y − 7 + 2y2 Side 3: 3y2 − 8 + 5y The perimeter of the quadrilateral is 8y3 − 2y2 + 4y − 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.

Answer 1

A. y^2 + 3y - 6 + 4y - 7 + 2y^2 + 3y^2 - 8 + 5y = 6y^2 + 12y - 21 <==

B. 8y^3 - 2y^2 + 4y - 26 - (6y^2 + 12y - 21) = 
    8y^3 - 2y^2 + 4y - 26 - 6y^2 - 12y + 21 = 
    8y^3 - 8y^2 - 8y + - 5 <==

C. (part A) this is closed under addition
     (part B) this is closed under subtraction
     Polynomials will be closed under an operation if the operation produces      another polynomial