The following table shows the length and width of a rectangle:
length width
rectangle a 4x + 5 3x − 2
which expression is the result of the perimeter of rectangle a and demonstrates the closure property?
14x + 6; the answer is a polynomial
14x + 6; the answer may or may not be a polynomial
2x + 6; the answer is a polynomial
2x + 6; the answer may or may not be a polynomial

the expression is 14x + 6; the answer is polynomial ⇒ 1st answer

step-by-step explanation:

* lets explain how to solve the problem

∵ the length of the rectangle is 4x + 5

∵ the width of the rectangle is 3x - 2

∵ the perimeter of the rectangle = 2(length) + 2(width)

- lets calculate the perimeter of the rectangle

∵ 2(length) = 2(4x + 5) = 2(4x) + 2(5) = 8x + 10

∴ 2(length) = 8x + 10

∵ 2(width) = 2(3x - 2) = 2(3x) - 2(2) = 6x - 4

∴ 2(width) = 6x - 4

∵ the perimeter = 2(length) + 2(width)

∴ the perimeter = 8x + 10 + 6x - 4

∴ the perimeter = (8x + 6x) + (10 - 4)

∴ the perimeter = 14x + 6

∵ 4x + 5 and 3x - 2 are polynomials

∵ the polynomials are closed under the addition

∵ polynomials will be closed under an operation if the operation

  produces another polynomial

∴ 14x + 6 is a polynomial

* the expression is 14x + 6; the answer is polynomial

yes the total will be same because in both of them the expression.is rearranged but their sign remains the same hence it hss just been shuffled

80

step-by-step explanation: