Question

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).

Answer 1

The area of the rectangle is $12x^{2} + 74x + 44$

The degree of the polynomial is 2nd degree and the classification of the polynomial is trinomial

The closure property of the polynomial is demonstrated as follows:

$(6x + 4) (2x + 11) = (2x + 11 )(6x + 4)$

The sides of the rectangle are (6x + 4) and (2x + 11). Therefore,

What is the area of a rectangle?

The area of the rectangle is,

$area = lw$

where,l = length,w = width.

Therefore, by using formula,

$area = (6x + 4)(2x + 11)$

$area = 12x^{2} + 66x + 8x + 44$

$area = 12x^{2} + 74x + 44$

b).The degree of the polynomial is 2nd degree and the classification of the polynomial is trinomial(it has three terms)

c).When something is closed, the output will be the same type of object as the inputs. Therefore, to demonstrate the closure property:

$(6x + 4) (2x + 11) = (2x + 11 )(6x + 4)$

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