anonymous
  • anonymous
can someone please help me with these question for a medal and fan?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
What are the parts that make up a polynomial expression and how are they used to classify polynomials? How are the properties of exponents used when multiplying or dividing two monomials? How is the distributive property used when finding the product of two polynomials?
anonymous
  • anonymous
polynomial can be either classified by number of terms or by degree
anonymous
  • anonymous
if by number of terms: This is a monomial \[3x^2\]and this is a binomial \[x^2 +2x\]

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anonymous
  • anonymous
3 terms = trinomial like \[x^2 +4x + 6\]
anonymous
  • anonymous
anything above are just call polynomial
anonymous
  • anonymous
ok so I understand how they are classified now thank you can you help with the other questions please
anonymous
  • anonymous
if we are classifying it by degree
anonymous
  • anonymous
\[2x^5\] is a 5th degree polymial and \[10x^2\] is a 2nd degree polynomial
anonymous
  • anonymous
when you divide same numbers with different powers you can just minus off the power, i.e: \[\frac{ 2^{10} }{ 2^4 } = 2^{10-4} = 2^6\]
anonymous
  • anonymous
its the same thing for multiply except you add the power
anonymous
  • anonymous
\[3^5 \times 3^7 = 3^{5+7} = 3^{12}\]
anonymous
  • anonymous
wait are you answering the second question
anonymous
  • anonymous
yea
anonymous
  • anonymous
I don't get it
anonymous
  • anonymous
which part?
anonymous
  • anonymous
I just don't understand the way that applies to the second question. could you try to re-explain it to me?
anonymous
  • anonymous
It says properties of exponents used in multiplying or dividing monomial
anonymous
  • anonymous
you understand whats an exponent?
anonymous
  • anonymous
yes
anonymous
  • anonymous
and monomial?
anonymous
  • anonymous
kinda could you explain that to me please
anonymous
  • anonymous
its a polynomial with a single term like\[3x\]\[2x^4\]
anonymous
  • anonymous
ok I get it
anonymous
  • anonymous
you have learn multiplying/dividing indices yet?
anonymous
  • anonymous
nope
anonymous
  • anonymous
ok it looks something like this
anonymous
  • anonymous
\[\frac{ 2^5 }{ 2^3 } = \frac{ 2 \times 2 \times 2 \times 2 \times 2 }{ 2 \times 2 \times 2 } \]
anonymous
  • anonymous
then you realize you can cancel 3 of the 2s out in the fraction so it becomes 2 x 2 which is 2^2
anonymous
  • anonymous
thats for dividing
anonymous
  • anonymous
ok I get it but it still doesn't give an answer to the second question
anonymous
  • anonymous
so in short you can just take the numerator power minus the denominator's one
anonymous
  • anonymous
its asking you to use that property of exponent in monomial
anonymous
  • anonymous
no its not it asking How are the properties of exponents used when multiplying or dividing two monomials?
anonymous
  • anonymous
its behaves the same way
anonymous
  • anonymous
as with normal integers
anonymous
  • anonymous
ok can I have help with the last question please
anonymous
  • anonymous
you know whats distributive property?
anonymous
  • anonymous
distributive property is like \[y(5x+y) = 5xy + y^2\]
anonymous
  • anonymous
as for the how part, we can multiply the terms from 1st polynomial with the 2nd
anonymous
  • anonymous
\[(a+b)(x+y) = ax + ay + bx + by\]
anonymous
  • anonymous
this pretty much explains it all
anonymous
  • anonymous
you can understand that?
anonymous
  • anonymous
no
anonymous
  • anonymous
ill do it with numbers \[2(3 + 4) = 2(3) + 2(4)\]
anonymous
  • anonymous
this is distributive property
anonymous
  • anonymous
I understand that that's distributive property but I still don't understand how to answer the question how does this go together with finding the product of two polynomials
anonymous
  • anonymous
When multiplying two polynomials together, we use the distributive property to multiply every term of one polynomial is multiplied times every term of the other polynomial then simplify your answer by combining any like terms.
anonymous
  • anonymous
sounds good?
anonymous
  • anonymous
yes thank you I was having the same problem trying to understand how what you said went together with the second question
anonymous
  • anonymous
ikr i have no problem doing questions but explaining is hella hard
anonymous
  • anonymous
could you just tell me the second question then so I can get this over with please
anonymous
  • anonymous
im finding sites to copy paste from lel
anonymous
  • anonymous
Exponents represent repeated multiplication, \[a \times a =a^2\]\[a^2 \times a^3 = (aa)(aaa) = a^{2+3} = a^5\]
anonymous
  • anonymous
you understand everything so far?
anonymous
  • anonymous
yes
anonymous
  • anonymous
i don't find any good paragraphs to copy paste so far, so you might need to demonstrate the properties
anonymous
  • anonymous
I don't think I will be aloud to do that you don't know the answer?
anonymous
  • anonymous
i don't know how to describe it
anonymous
  • anonymous
When monomials include both a number and a variable, the number is called the coefficient. For example, in the monomial 8x2, 8 is the coefficient. The variables in a monomial can have whole number exponents, but no negative exponents. Just as numbers can be multiplied and divided, monomials with variables can also be multiplied and divided following the same rules.
anonymous
  • anonymous
this might be the best i found so far
anonymous
  • anonymous
thanks
anonymous
  • anonymous
yw

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