- anonymous

please help
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 to receive full credit. (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)

- jamiebookeater

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- Mertsj

|dw:1438825943675:dw|

- anonymous

wait do i add like terms or foil this?

- anonymous

oh nvm

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## More answers

- anonymous

can you help with part b ?

- anonymous

- anonymous

i was supposed to foil right?

- anonymous

- Mertsj

yes. to multiply two binomials, use FOIL

- anonymous

the answer i got is 12x+66x+8x+44

- anonymous

is that correct?

- Mertsj

What is x times x?

- anonymous

o so x^2?

- Mertsj

yes

- anonymous

12x^2+66x^2+8x+44?

- Mertsj

|dw:1438826570048:dw|

- anonymous

ok i understand can you explain part b please

- Mertsj

|dw:1438826654711:dw|

- Mertsj

The highest exponent is 2 so it is degree 2
There are three terms so it is a trinomial

- anonymous

thank you very much can you help with part c and explain it a little more i dont just want the answers

- anonymous

- mathstudent55

I'll explain the closure property with these examples:
1. The closure property applies to the multiplication of integers because when any two integers are multiplied together, the product is an integer. For example 5 * 2 = 10. 5, 2, and 10 are all integers.
2. The closure property does not apply to the division of integers because not every division of integers results in an integer. Fro example, 5/2 = 2.5. 5 and 2 are integers, but 2.5 is not.

- anonymous

this is difficult for me to relate to my problem

- anonymous

because i need the closure property of polynomials

- mathstudent55

Well, if you multiply polynomials, is the result always a polynomial?
If so, there is closure. If not, there isn't.

- Mertsj

The closure property for multiplication says if you multiply two integers you get an integer so the set of integers is closed for multiplication.

- Mertsj

The closure property for natural numbers says that if you multiply two natural numbers you get a natural number so the set of natural numbers is said to be closed for multiplication.

- Mertsj

The closure property for rational numbers says that if you multiply two rational numbers you will get a rational number so the set of rational numbers is said to be closed for multiplication.

- Mertsj

What do you suppose the closure property for polynomials would be?

- mathstudent55

I'll show you an example of an operation that is not closed.
Let's look at division of polynomials.
\(\dfrac{5x^2 + 2x - 8}{x} = 5x + 2 - \dfrac{8}{x}\)
The quotient is not a polynomial, so polynomials are not closed for division.

- anonymous

it would be if you multiply to polynomials you will get another polynomial so the set would be closed

- Mertsj

Did that work in your example? is 6x+4 a polynomial?

- Mertsj

Is 2x+11 a polynomial?

- Mertsj

When you multiplied them you got 12x^2+74x+44
Is that a polynomial?

- Mertsj

Why aren't you answering my questions?

- anonymous

no thats a trinomial

- Mertsj

Is a trinomial a member of the family of polynomials?

- anonymous

yes i think so

- Mertsj

monomials, binomials, trinomials, four term polynomials...they are all polynomials

- Mertsj

Just like Chinese, Japanese, and Mexicans are all human beings.

- anonymous

yes i get it now so it demonstrates it when i multiply the terms and still get a polynomial?

- Mertsj

6x+4 is a binomial and therefore is a polynomial.
2x+11 is a binomial and therefore is a polynomial.
12x^2+74x+44 is a trinomial and therefore is a polynomial.

- anonymous

thnk you so much i got my answer i really appreciate it

- Mertsj

So you have shown, at least in this case, that the set of polynomials appears to be closed for multiplication because you multiplied two polynomials and got a polynomial.

- Mertsj

yw

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