A rectangle has sides measuring (2x + 7) units and (5x + 9) units.

Part A: What is the expression that represents the area of the rectangle? Show your work. (4 points)

Part B: What are the degree and classification of the expression obtained in Part A? (3 points)

Part C: How does Part A demonstrate the closure property for polynomials? (3 points)

1. The expression for the area of the rectangle is + 53x + 63.

2. The expression is second degree (quadratic) and it can be classified as binomial.

3. Part A demonstrates that the expression is closed under addition as the closure property for the polynomial, + 53x + 63.

Step-by-step explanation:

Area of a rectangle = length × width

Assuming in the given rectangle, the length is (5x + 9) units and width is (2x + 7) units.

1. Area = (5x + 9) × (2x + 7)

       = 5x(2x + 7) + 9(2x + 7)

       = + 35x + 18x + 63

      = + 53x + 63

The expression for the area of the rectangle is + 53x + 63.

2. The expression is second degree (quadratic) and it can be classified as binomial.

3. The closure property explains that when an arithmetical operation is performed on any two numbers in a set, the result is another number in the same set.

Part A demonstrates that the expression is closed under addition as the closure property for the polynomial, + 53x + 63.

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