Question 3 (essay worth 10 points) (06.01, 06.04 mc) a rectangle has sides measuring (6x + 4) units and (2x + 11) 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)

  A: 12x² +74x +44

  B: degree 2 trinomial

  C: the product of two polynomials is a polynomial

Step-by-step explanation:

A: The area is the product of length and width, so will be the product ...

  (6x +4)(2x +11) = 6x(2x +11) +4(2x +11) = 12x² +66x +8x +44

  = 12x² +74x +44

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B: The highest power of x is 2, so this is a 2nd-degree polynomial. It has 3 terms, so is classified as a trinomial.

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C: In part A we multiplied two polynomials and obtained a result that is a polynomial. The closure property of multiplication on a set requires that any product of members of the set also is a member of the set. Thus the closure property of multiplication on the set of polynomials is not violated by the answer to part A.

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Closure for one product does not demonstrate closure. It provides an example for which closure is not violated.

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