Question

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

Answer 1

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?

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

anything above are just call polynomial

Answer 6

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

Answer 7

if we are classifying it by degree

Answer 8

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

Answer 9

when you divide same numbers with different powers you can just minus off the power, i.e: \[\frac{ 2^{10} }{ 2^4 } = 2^{10-4} = 2^6\]

Answer 10

its the same thing for multiply except you add the power

Answer 11

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

Answer 12

wait are you answering the second question

Answer 13

yea

Answer 14

I don't get it

Answer 15

which part?

Answer 16

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

Answer 17

It says properties of exponents used in multiplying or dividing monomial

Answer 18

you understand whats an exponent?

Answer 19

yes

Answer 20

and monomial?

Answer 21

kinda could you explain that to me please

Answer 22

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

Answer 23

ok I get it

Answer 24

you have learn multiplying/dividing indices yet?

Answer 25

nope

Answer 26

ok it looks something like this

Answer 27

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

Answer 28

then you realize you can cancel 3 of the 2s out in the fraction so it becomes 2 x 2 which is 2^2

Answer 29

thats for dividing

Answer 30

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

Answer 31

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

Answer 32

its asking you to use that property of exponent in monomial

Answer 33

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

Answer 34

its behaves the same way

Answer 35

as with normal integers

Answer 36

ok can I have help with the last question please

Answer 37

you know whats distributive property?

Answer 38

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

Answer 39

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

Answer 40

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

Answer 41

this pretty much explains it all

Answer 42

you can understand that?

Answer 43

no

Answer 44

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

Answer 45

this is distributive property

Answer 46

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

Answer 47

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.

Answer 48

sounds good?

Answer 49

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

Answer 50

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

Answer 51

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

Answer 52

im finding sites to copy paste from lel

Answer 53

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

Answer 54

you understand everything so far?

Answer 55

yes

Answer 56

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

Answer 57

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

Answer 58

i don't know how to describe it

Answer 59

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.

Answer 60

this might be the best i found so far

Answer 61

thanks

Answer 62

yw