Question

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)

Answer 1

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

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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

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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.