Organize the following polynomial expressions from least to greatest based on their degree:
x + 2xyz
9x3y2
18x2 + 5ab − 6y
4x4 + 3x2 − x − 4

- lalaland_lauren

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- anonymous

\[x + 2xyz=x + 2x^1y^1z^1\] has degree \(1+1+1=3\)

- anonymous

\[9x^3y^2\] has degree \(3+2=5\)

- anonymous

i bet you can do the rest

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## More answers

- anonymous

if not, i can check

- lalaland_lauren

would this be number three?
\[18^2 +5a^1b^1-6y^-1\]

- lalaland_lauren

that's -6y^1 but I think the one is negative

- anonymous

\[18x^2 + 5ab − 6y\] has degree 2

- lalaland_lauren

oh okay so if it doesn't show an exponent then you kind of make your own

- anonymous

yeah i have a feeling you don't quite get this
am i right?

- lalaland_lauren

yup

- anonymous

ok here is a polynomial with three terms
\[xy^2+x^2y^2+2xy\]

- anonymous

each term has a degree '
the degree of
\[xy^2\] is \[1+2=3\] th degree of \(x^2y^2\) is \(2+2=4\) and the degree of \(2xy\) is \(1+1=2\)

- lalaland_lauren

so the degrees are the exponents added up

- anonymous

the "degree of the polynomial" is the degree of the term of highest degree, so the degree of
\[xy^2+x^2y^2+2xy\] is \(4\)

- anonymous

yes, the degree of each term is the sum of the degrees of each variable
so for example the degree of \(xy^2z^4\) is \(7\)

- lalaland_lauren

and whichever has the highest degree is the degree of the polynomial?

- lalaland_lauren

sorry if I repeat things, just trying to get it through to myself

- anonymous

that is fine

- anonymous

you are right, the degree of the polynomial is the degree of the term of highest degree

- anonymous

so for example if you just have on variable, the degree of say \[2x^5+3x^2+5x+1\] is \(5\)
but if you have more than one variable you have to add the degrees of each variable

- anonymous

with that in mind, what is the degree of
\[4x^4 + 3x^2 − x − 4\]?

- lalaland_lauren

the degree of the polynomial would be 4 because of 4x^4

- anonymous

yes

- lalaland_lauren

\[4x^4+3x^2-x-4\]
first set has a degree of four, second set has a degree of two, and the third I think it's one but I'm not sure if it's negative one

- anonymous

a polynomial cannot have a term of negative degree

- lalaland_lauren

x + 2xyz
degree of 3
9x3y2
degree of 5
18x2 + 5ab − 6y
degree of 2 I'm pretty sure
4x4 + 3x2 − x − 4
4

- anonymous

yes

- lalaland_lauren

okay gotcha

- anonymous

btw the degree of a constant is zero

- lalaland_lauren

III, I, IV, II
IV, I, II, III
III, II, IV, I
IV, III, I, II
these were the answer choices btw lol

- lalaland_lauren

what's a constant?

- anonymous

lol i will let you order them yourself, you got them all right

- lalaland_lauren

it's a

- anonymous

\[x^2-5x+\color{red}3\] the constant is \(\color{red}3\)

- anonymous

yeah it is A

- lalaland_lauren

so one with no exponent or variable, just a flat out number

- anonymous

right
called a "constant" because it does not depend of what \(x\) is

- anonymous

i have a question
do you know what \\[2x^3+5x^2+4x+7\] is if \(x=10\)?

- lalaland_lauren

\[2(10)^3+5(10)^2+4(10)+7\]
\[2(1,000)+5(100)+40+7\]
two thousand five hundred and forty seven

- anonymous

right
so you see we write our whole numbers as polynomials, using base ten (instead of x)

- anonymous

\[2(10)^3+5(10)^2+4(10)+7=2547\]

- anonymous

keep that in mind when you learn to add, subtract and multiply polynomials
it works pretty much the same way as with whole numbers
of course there are some differences, but it is basically the same

- lalaland_lauren

okay :-) can you help me with some more questions?

- lalaland_lauren

it's like two or three more, one I think I got down

- anonymous

sure

- lalaland_lauren

4x^2 + 3xy + 12yz
this would be a second degree trinomial correct?

- anonymous

yes

- lalaland_lauren

okay that's what I put, next one

- lalaland_lauren

Organize the following expressions from greatest to least by number of terms:
x + 2xyz
9x2yz
18x2 + 5ab − 6y
4x3 + 3x2 − x − 4
Answers:
III, IV, I, II
IV, I, II, III
IV, III, I, II
III, II, IV, I

- lalaland_lauren

Is it C?

- lalaland_lauren

Because I think that terms are the sets in the polynomial

- anonymous

the "number of terms"? yeah we can count for sure

- anonymous

you are right, it is C

- lalaland_lauren

Which statement best demonstrates why the following is a non-example of a polynomial?
\[\frac{ 33y^2 }{ x^2 } - 62y^2xz-35z^2y^2\]
The expression has a variable raised to a negative exponent.
The expression has a negative coefficient.
The expression has a variable raised to a fraction.
The expression has a variable in the denominator of a fraction.

- lalaland_lauren

I feel like it's C again

- anonymous

not this time

- anonymous

a polynomial cannot have a variable in the denominator

- anonymous

" The expression has a variable raised to a fraction." actually makes no sense at all
go with D

- lalaland_lauren

oh okay, I thought fractions weren't supposed to be in polynomials period lol

- anonymous

unless it means something iike
\[x^{\frac{2}{3}}\]which is NOT a polynomial

- anonymous

the coeficients can be fractions
\[\frac{4}{5}x^2\] is a polynomial

- lalaland_lauren

Last one :)
Which of the following shows 9x^2y − 4x + 3y^3x − 2y^2 written in standard form?
9x^2y − 4x + 3y^3x − 2y^2
3y^3x − 2y^2 + 9x^2y − 4x
9x^2y − 4x − 2y^2 + 3y^3x
3y^3x + 9x^2y − 2y^2 − 4x

- anonymous

standard form means order the terms from highest degree to lowest degree

- lalaland_lauren

Then D

- anonymous

yes

- lalaland_lauren

I got a one hundred, thank you so much!!

- anonymous

yay
yw
see you in lala land

- lalaland_lauren

Lol! I'll probably need help tomorrow, will you still be on?

- anonymous

always glad to help someone who is actually trying

- anonymous

probably
you can always tag me if you like

- lalaland_lauren

Okay :) thank you so much, I have to go to sleep now. Good night!

- anonymous

sometime around 9:30 or 10 usually
gnight

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