Ineed this answered as quick as possible, . 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)

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.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2