(plz stat) the lengths of three sides of a trapezoid are shown below: side 1: 16z2 − 4z + 2 side 2: −2z + 21 + 7z2 side 3: 2 − 3z + 18z2 the perimeter of the trapezoid is 17z3 + 60z2 + 2z − 5. 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)

Hey there :)

The perimeter formula of a trapezium is:
P = a + b + c + d ( adding all sides )

Perimeter is given : P = 17z³ + 60z² + 2z - 5

Part A :

Total lengths of sides 1, 2 and 3 will be just adding the given lengths : 
1 → 16z² - 4z + 2
2 → 7z² - 2z + 21
3 → 18z² - 3z + 2

side 1 + side 2 + side 3
( 16z² - 4z + 2 ) + ( 7z² - 2z + 21 ) + ( 18z² - 3z + 2 )

Combine like terms together:

16z² + 7z² + 18z² - 4z - 2z - 3z + 2 +21 + 2
41z² - 9z + 25

Part B:

Length of 4th side will be the total perimeter minus the total length of sides 1, 2 and 3:

( 17z³ + 60z² + 2z - 5 ) - ( 41z² - 9z + 25 )

Combine like terms

17z³ + 60z² - 41z² + 2z + 9z - 5 - 25
17z³ + 19z² + 11z - 30

Part C:

Addition of polynomials result in polynomials as well as subtraction of polynomials result in polynomials.

Therefore, this polynomial is closed under addition and subtraction. 

The slope of the function is 0.5.