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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)

Respuesta :

kileysillygoose

Answer:

A: 10x^2 +53x +63   B: degree 2; quadratic trinomial  C: the result of the multiplication of polynomials is a polynomial

Step-by-step explanation:

Part A:

The area is the product of length and width. The distributive property is useful for simplifying the expression.

 A = LW

 A = (2x +7)(5x +9) = 2x(5x +9) +7(5x +9)

 A = (10x^2 +18x) +(35x +63)

 A = 10x^2 +53x +63 . . . . area expression

Part B:

The highest power of x is 2. There are 3 terms. A degree-2 polynomial is called a "quadratic." A 3-term polynomial is called a "trinomial."

degree 2

quadratic trinomial

Part C:

In part A we multiplied two polynomials and came up with a result that is a polynomial. This suggests polynomials are closed with respect to multiplication.

I hope this helps!!

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