can someone please help me with these question for a medal and fan?

- anonymous

can someone please help me with these question for a medal and fan?

- katieb

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- 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

polynomial can be either classified by number of terms or by degree

- anonymous

if by number of terms:
This is a monomial \[3x^2\]and this is a binomial \[x^2 +2x\]

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## More answers

- anonymous

3 terms = trinomial like \[x^2 +4x + 6\]

- anonymous

anything above are just call polynomial

- anonymous

ok so I understand how they are classified now thank you can you help with the other questions please

- anonymous

if we are classifying it by degree

- anonymous

\[2x^5\] is a 5th degree polymial and \[10x^2\] is a 2nd degree polynomial

- 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

its the same thing for multiply except you add the power

- anonymous

\[3^5 \times 3^7 = 3^{5+7} = 3^{12}\]

- anonymous

wait are you answering the second question

- anonymous

yea

- anonymous

I don't get it

- anonymous

which part?

- anonymous

I just don't understand the way that applies to the second question. could you try to re-explain it to me?

- anonymous

It says properties of exponents used in multiplying or dividing monomial

- anonymous

you understand whats an exponent?

- anonymous

yes

- anonymous

and monomial?

- anonymous

kinda could you explain that to me please

- anonymous

its a polynomial with a single term like\[3x\]\[2x^4\]

- anonymous

ok I get it

- anonymous

you have learn multiplying/dividing indices yet?

- anonymous

nope

- anonymous

ok it looks something like this

- anonymous

\[\frac{ 2^5 }{ 2^3 } = \frac{ 2 \times 2 \times 2 \times 2 \times 2 }{ 2 \times 2 \times 2 } \]

- 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

thats for dividing

- anonymous

ok I get it but it still doesn't give an answer to the second question

- anonymous

so in short you can just take the numerator power minus the denominator's one

- anonymous

its asking you to use that property of exponent in monomial

- anonymous

no its not it asking How are the properties of exponents used when multiplying or dividing two monomials?

- anonymous

its behaves the same way

- anonymous

as with normal integers

- anonymous

ok can I have help with the last question please

- anonymous

you know whats distributive property?

- anonymous

distributive property is like \[y(5x+y) = 5xy + y^2\]

- anonymous

as for the how part, we can multiply the terms from 1st polynomial with the 2nd

- anonymous

\[(a+b)(x+y) = ax + ay + bx + by\]

- anonymous

this pretty much explains it all

- anonymous

you can understand that?

- anonymous

no

- anonymous

ill do it with numbers \[2(3 + 4) = 2(3) + 2(4)\]

- anonymous

this is distributive property

- 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

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

sounds good?

- anonymous

yes thank you I was having the same problem trying to understand how what you said went together with the second question

- anonymous

ikr i have no problem doing questions but explaining is hella hard

- anonymous

could you just tell me the second question then so I can get this over with please

- anonymous

im finding sites to copy paste from lel

- anonymous

Exponents represent repeated multiplication,
\[a \times a =a^2\]\[a^2 \times a^3 = (aa)(aaa) = a^{2+3} = a^5\]

- anonymous

you understand everything so far?

- anonymous

yes

- anonymous

i don't find any good paragraphs to copy paste so far, so you might need to demonstrate the properties

- anonymous

I don't think I will be aloud to do that you don't know the answer?

- anonymous

i don't know how to describe it

- 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

this might be the best i found so far

- anonymous

thanks

- anonymous

yw

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