lalaland_lauren
  • lalaland_lauren
Organize the following polynomial expressions from least to greatest based on their degree: x + 2xyz 9x3y2 18x2 + 5ab − 6y 4x4 + 3x2 − x − 4
Algebra
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
\[x + 2xyz=x + 2x^1y^1z^1\] has degree \(1+1+1=3\)
anonymous
  • anonymous
\[9x^3y^2\] has degree \(3+2=5\)
anonymous
  • anonymous
i bet you can do the rest

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anonymous
  • anonymous
if not, i can check
lalaland_lauren
  • lalaland_lauren
would this be number three? \[18^2 +5a^1b^1-6y^-1\]
lalaland_lauren
  • lalaland_lauren
that's -6y^1 but I think the one is negative
anonymous
  • anonymous
\[18x^2 + 5ab − 6y\] has degree 2
lalaland_lauren
  • lalaland_lauren
oh okay so if it doesn't show an exponent then you kind of make your own
anonymous
  • anonymous
yeah i have a feeling you don't quite get this am i right?
lalaland_lauren
  • lalaland_lauren
yup
anonymous
  • anonymous
ok here is a polynomial with three terms \[xy^2+x^2y^2+2xy\]
anonymous
  • 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
  • lalaland_lauren
so the degrees are the exponents added up
anonymous
  • 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
  • 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
  • lalaland_lauren
and whichever has the highest degree is the degree of the polynomial?
lalaland_lauren
  • lalaland_lauren
sorry if I repeat things, just trying to get it through to myself
anonymous
  • anonymous
that is fine
anonymous
  • anonymous
you are right, the degree of the polynomial is the degree of the term of highest degree
anonymous
  • 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
  • anonymous
with that in mind, what is the degree of \[4x^4 + 3x^2 − x − 4\]?
lalaland_lauren
  • lalaland_lauren
the degree of the polynomial would be 4 because of 4x^4
anonymous
  • anonymous
yes
lalaland_lauren
  • 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
  • anonymous
a polynomial cannot have a term of negative degree
lalaland_lauren
  • 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
  • anonymous
yes
lalaland_lauren
  • lalaland_lauren
okay gotcha
anonymous
  • anonymous
btw the degree of a constant is zero
lalaland_lauren
  • 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
  • lalaland_lauren
what's a constant?
anonymous
  • anonymous
lol i will let you order them yourself, you got them all right
lalaland_lauren
  • lalaland_lauren
it's a
anonymous
  • anonymous
\[x^2-5x+\color{red}3\] the constant is \(\color{red}3\)
anonymous
  • anonymous
yeah it is A
lalaland_lauren
  • lalaland_lauren
so one with no exponent or variable, just a flat out number
anonymous
  • anonymous
right called a "constant" because it does not depend of what \(x\) is
anonymous
  • anonymous
i have a question do you know what \\[2x^3+5x^2+4x+7\] is if \(x=10\)?
lalaland_lauren
  • 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
  • anonymous
right so you see we write our whole numbers as polynomials, using base ten (instead of x)
anonymous
  • anonymous
\[2(10)^3+5(10)^2+4(10)+7=2547\]
anonymous
  • 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
  • lalaland_lauren
okay :-) can you help me with some more questions?
lalaland_lauren
  • lalaland_lauren
it's like two or three more, one I think I got down
anonymous
  • anonymous
sure
lalaland_lauren
  • lalaland_lauren
4x^2 + 3xy + 12yz this would be a second degree trinomial correct?
anonymous
  • anonymous
yes
lalaland_lauren
  • lalaland_lauren
okay that's what I put, next one
lalaland_lauren
  • 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
  • lalaland_lauren
Is it C?
lalaland_lauren
  • lalaland_lauren
Because I think that terms are the sets in the polynomial
anonymous
  • anonymous
the "number of terms"? yeah we can count for sure
anonymous
  • anonymous
you are right, it is C
lalaland_lauren
  • 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
  • lalaland_lauren
I feel like it's C again
anonymous
  • anonymous
not this time
anonymous
  • anonymous
a polynomial cannot have a variable in the denominator
anonymous
  • anonymous
" The expression has a variable raised to a fraction." actually makes no sense at all go with D
lalaland_lauren
  • lalaland_lauren
oh okay, I thought fractions weren't supposed to be in polynomials period lol
anonymous
  • anonymous
unless it means something iike \[x^{\frac{2}{3}}\]which is NOT a polynomial
anonymous
  • anonymous
the coeficients can be fractions \[\frac{4}{5}x^2\] is a polynomial
lalaland_lauren
  • 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
  • anonymous
standard form means order the terms from highest degree to lowest degree
lalaland_lauren
  • lalaland_lauren
Then D
anonymous
  • anonymous
yes
lalaland_lauren
  • lalaland_lauren
I got a one hundred, thank you so much!!
anonymous
  • anonymous
yay yw see you in lala land
lalaland_lauren
  • lalaland_lauren
Lol! I'll probably need help tomorrow, will you still be on?
anonymous
  • anonymous
always glad to help someone who is actually trying
anonymous
  • anonymous
probably you can always tag me if you like
lalaland_lauren
  • lalaland_lauren
Okay :) thank you so much, I have to go to sleep now. Good night!
anonymous
  • anonymous
sometime around 9:30 or 10 usually gnight

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