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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)

Respuesta :

Answer:

Part A = 36z² - 9z + 8

Part B = 5z³ + 4z² + 16z - 23

Part c = Yes.

Step-by-step explanation:

Polynomials : Polynomials are algebraic expressions that consist of variables and coefficients.

Trapezium: A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other.

Given the length of sides :

Side 1: 11z² - 4z + 2

Side 2: -2z + 3 + 12z²

Side 3: 3 - 3z + 13z²

and The perimeter of the trapezoid is 5z³ + 40z² + 7z - 15.

PART A:

The total length of sides 1, 2, and 3 of the trapezoid is obtained by the sum of the trapezoid :

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

11z² - 4z + 2 - 2z + 3 + 12z² + 3 - 3z + 13z²

36z² - 9z + 8

PART B:

The length of the fourth side of the trapezoid is given by the difference between the perimeter of the trapezoid and the sum of  length of sides 1, 2, and 3.

5z³ + 40z² + 7z - 15 - 36z² + 9z - 8

5z³ + 4z² + 16z - 23

PART C:

From part A, we can see that the addition of polynomials results in a polynomial.

Likewise, the subtraction of polynomials results in a polynomial.

Therefore, we can say that the polynomials are closed under addition and subtraction.

learn more about polynomials and quadrilaterals at

https://brainly.com/question/15301188

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