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

Answer 2

Answer:

Part A: 12y^2+9y-21

Part B: 4y^2+6y^2+7y-5

Part C:  A set of numbers is closed, or has closure, under a given operation if the result of the operation on any two numbers in the set is also in the set. For example, the set of real numbers is closed under addition, because adding any two real numbers results in another real number. Likewise, the real numbers are closed under subtraction, multiplication and division (by a nonzero real number), because performing these operations on two real numbers always yields another real number. Polynomials are closed under the same operations as integers.

Step-by-step explanation:

Hope this helps!!