anonymous
  • 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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Mertsj
  • Mertsj
|dw:1438825943675:dw|
anonymous
  • anonymous
wait do i add like terms or foil this?
anonymous
  • anonymous
oh nvm

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anonymous
  • anonymous
can you help with part b ?
anonymous
  • anonymous
@Mertsj
anonymous
  • anonymous
i was supposed to foil right?
anonymous
  • anonymous
@jim_thompson5910
Mertsj
  • Mertsj
yes. to multiply two binomials, use FOIL
anonymous
  • anonymous
the answer i got is 12x+66x+8x+44
anonymous
  • anonymous
is that correct?
Mertsj
  • Mertsj
What is x times x?
anonymous
  • anonymous
o so x^2?
Mertsj
  • Mertsj
yes
anonymous
  • anonymous
12x^2+66x^2+8x+44?
Mertsj
  • Mertsj
|dw:1438826570048:dw|
anonymous
  • anonymous
ok i understand can you explain part b please
Mertsj
  • Mertsj
|dw:1438826654711:dw|
Mertsj
  • Mertsj
The highest exponent is 2 so it is degree 2 There are three terms so it is a trinomial
anonymous
  • anonymous
thank you very much can you help with part c and explain it a little more i dont just want the answers
anonymous
  • anonymous
@Mertsj
mathstudent55
  • 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
  • anonymous
this is difficult for me to relate to my problem
anonymous
  • anonymous
because i need the closure property of polynomials
mathstudent55
  • mathstudent55
Well, if you multiply polynomials, is the result always a polynomial? If so, there is closure. If not, there isn't.
Mertsj
  • 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
  • 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
  • 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
  • Mertsj
What do you suppose the closure property for polynomials would be?
mathstudent55
  • 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
  • anonymous
it would be if you multiply to polynomials you will get another polynomial so the set would be closed
Mertsj
  • Mertsj
Did that work in your example? is 6x+4 a polynomial?
Mertsj
  • Mertsj
Is 2x+11 a polynomial?
Mertsj
  • Mertsj
When you multiplied them you got 12x^2+74x+44 Is that a polynomial?
Mertsj
  • Mertsj
Why aren't you answering my questions?
anonymous
  • anonymous
no thats a trinomial
Mertsj
  • Mertsj
Is a trinomial a member of the family of polynomials?
anonymous
  • anonymous
yes i think so
Mertsj
  • Mertsj
monomials, binomials, trinomials, four term polynomials...they are all polynomials
Mertsj
  • Mertsj
Just like Chinese, Japanese, and Mexicans are all human beings.
anonymous
  • anonymous
yes i get it now so it demonstrates it when i multiply the terms and still get a polynomial?
Mertsj
  • 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
  • anonymous
thnk you so much i got my answer i really appreciate it
Mertsj
  • 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
  • Mertsj
yw

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