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I need this answered as quick as possible, please. Thank you! Will award Brainliest.
The lengths of three sides of a trapezoid are shown below:
Side 1: 11z2 − 4z + 2
Side 2: −2z + 3 + 12z2
Side 3: 3 − 3z + 13z2
The perimeter of the trapezoid is 5z3 + 40z2 + 7z − 15.
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)

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smmwaite

Answers

Part 1: 36z²-9z+8

Part 2: 5z³+4z²+16z-23

Part 3: Yes


Explanation

Part 1

(11z²-4z+2) + (-2z+3+12z²) + (3-3z+13z²) = 11z²+12z²+13z²-4z-2z-3z+2+3+3

= 36z²-9z+8


Part 2

(5z³ + 40z² + 7z − 15) - (36z²-9z+8) = 5z³ +40z²-36z²+7z+9z-15-8

=5z³+4z²+16z-23


Part 3

Yes.

The polynomials 5z³+4z²+16z-23 and 36z²-9z+8 form a system analogous to the integers, which are closed under the operations of addition and subtraction.



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