Question

Organize the following polynomial expressions from least to greatest based on their degree:


x + 2xyz
9x3y2
18x2 + 5ab − 6y
4x4 + 3x2 − x − 4

Answer 1

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

Answer 2

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

Answer 3

i bet you can do the rest

Answer 4

if not, i can check

Answer 5

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

Answer 6

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

Answer 7

\[18x^2 + 5ab − 6y\] has degree 2

Answer 8

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

Answer 9

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

Answer 10

yup

Answer 11

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

Answer 12

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 \(1+1=2\)

Answer 13

so the degrees are the exponents added up

Answer 14

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 \(4\)

Answer 15

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 \(7\)

Answer 16

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

Answer 17

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

Answer 18

that is fine

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

yes

Answer 24

\[4x^4+3x^2-x-4\]
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

Answer 25

a polynomial cannot have a term of negative degree

Answer 26

x + 2xyz
degree of 3

9x3y2
degree of 5

18x2 + 5ab − 6y
degree of 2 I'm pretty sure

4x4 + 3x2 − x − 4
4

Answer 27

yes

Answer 28

okay gotcha

Answer 29

btw the degree of a constant is zero

Answer 30

III, I, IV, II
IV, I, II, III
III, II, IV, I
IV, III, I, II

these were the answer choices btw lol

Answer 31

what's a constant?

Answer 32

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

Answer 33

it's a

Answer 34

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

Answer 35

yeah it is A

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

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

Answer 43

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

Answer 44

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

Answer 45

sure

Answer 46

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

Answer 47

yes

Answer 48

okay that's what I put, next one

Answer 49

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

Answer 50

Is it C?

Answer 51

Because I think that terms are the sets in the polynomial

Answer 52

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

Answer 53

you are right, it is C

Answer 54

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.

Answer 55

I feel like it's C again

Answer 56

not this time

Answer 57

a polynomial cannot have a variable in the denominator

Answer 58

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

Answer 59

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

Answer 60

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

Answer 61

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

Answer 62

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

Answer 63

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

Answer 64

Then D

Answer 65

yes

Answer 66

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

Answer 67

yay
yw
see you in lala land

Answer 68

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

Answer 69

always glad to help someone who is actually trying

Answer 70

probably
you can always tag me if you like

Answer 71

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

Answer 72

sometime around 9:30 or 10 usually
gnight