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)
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Answer 1

A rectangle has sides measuring (6x + 4) units and (2x + 11) units.

Area of the rectangle =$12x^2+74x+44$

Degree is 2 and it is a trinomial

To find out the area we multiplied two binomials . It demonstrate the closure property

Given :

A rectangle has sides measuring (6x + 4) units and (2x + 11) units.

Area of the rectangle is length times width

length is 6x+4  and width is 2x+11

We multiply it to find the area

$Area =(6x+4)(2x+11)\\Area = 6x\cdot \:2x+6x\cdot \:11+4\cdot \:2x+4\cdot \:11\\combine \; like \; terms\\Area =12x^2+74x+44$

Expression for the area of the rectangle is $12x^2+74x+44$

Degree is the highest exponent

In that expression the highest exponent is 2 and it has three terms

Degree is 2   and it is a trinomial expression

Closure property says that if an operation produces another polynomial then the polynomial will be closed under operation

To find out the area we multiplied two binomials

$\left(6x+4\right)\left(2x+11\right)$

It demonstrate the closure property

Learn more : brainly.com/question/22811803

Answer 2

A rectangle has sides measuring (6x + 4) units and (2x + 11) units.

Area of the rectangle =

The Degree is 2 and it is a trinomial

To find out the area we multiplied two binomials. It demonstrates the closure of property

Given :

A rectangle has sides measuring (6x + 4) units and (2x + 11) units.

The Area of the rectangle is length times width

length is 6x+4  and width is 2x+11

We multiply it to find the area

Expression for the area of the rectangle is  

The Degree is the highest exponent

In that expression, the highest exponent is 2 and it has three terms

The Degree is 2   and it is a trinomial expression

Closure property says that if an operation produces another polynomial then the polynomial will be closed under an operation

To find out the area we multiplied two binomials

It demonstrates the closure of the property

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