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lalaland_lauren

  • one year ago

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

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  1. anonymous
    • one year ago
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    \[x + 2xyz=x + 2x^1y^1z^1\] has degree \(1+1+1=3\)

  2. anonymous
    • one year ago
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    \[9x^3y^2\] has degree \(3+2=5\)

  3. anonymous
    • one year ago
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    i bet you can do the rest

  4. anonymous
    • one year ago
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    if not, i can check

  5. lalaland_lauren
    • one year ago
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    would this be number three? \[18^2 +5a^1b^1-6y^-1\]

  6. lalaland_lauren
    • one year ago
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    that's -6y^1 but I think the one is negative

  7. anonymous
    • one year ago
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    \[18x^2 + 5ab − 6y\] has degree 2

  8. lalaland_lauren
    • one year ago
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    oh okay so if it doesn't show an exponent then you kind of make your own

  9. anonymous
    • one year ago
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    yeah i have a feeling you don't quite get this am i right?

  10. lalaland_lauren
    • one year ago
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    yup

  11. anonymous
    • one year ago
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    ok here is a polynomial with three terms \[xy^2+x^2y^2+2xy\]

  12. anonymous
    • one year ago
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    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 \(1+1=2\)

  13. lalaland_lauren
    • one year ago
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    so the degrees are the exponents added up

  14. anonymous
    • one year ago
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    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 \(4\)

  15. anonymous
    • one year ago
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    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 \(7\)

  16. lalaland_lauren
    • one year ago
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    and whichever has the highest degree is the degree of the polynomial?

  17. lalaland_lauren
    • one year ago
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    sorry if I repeat things, just trying to get it through to myself

  18. anonymous
    • one year ago
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    that is fine

  19. anonymous
    • one year ago
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    you are right, the degree of the polynomial is the degree of the term of highest degree

  20. anonymous
    • one year ago
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    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

  21. anonymous
    • one year ago
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    with that in mind, what is the degree of \[4x^4 + 3x^2 − x − 4\]?

  22. lalaland_lauren
    • one year ago
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    the degree of the polynomial would be 4 because of 4x^4

  23. anonymous
    • one year ago
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    yes

  24. lalaland_lauren
    • one year ago
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    \[4x^4+3x^2-x-4\] 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

  25. anonymous
    • one year ago
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    a polynomial cannot have a term of negative degree

  26. lalaland_lauren
    • one year ago
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    x + 2xyz degree of 3 9x3y2 degree of 5 18x2 + 5ab − 6y degree of 2 I'm pretty sure 4x4 + 3x2 − x − 4 4

  27. anonymous
    • one year ago
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    yes

  28. lalaland_lauren
    • one year ago
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    okay gotcha

  29. anonymous
    • one year ago
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    btw the degree of a constant is zero

  30. lalaland_lauren
    • one year ago
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    III, I, IV, II IV, I, II, III III, II, IV, I IV, III, I, II these were the answer choices btw lol

  31. lalaland_lauren
    • one year ago
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    what's a constant?

  32. anonymous
    • one year ago
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    lol i will let you order them yourself, you got them all right

  33. lalaland_lauren
    • one year ago
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    it's a

  34. anonymous
    • one year ago
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    \[x^2-5x+\color{red}3\] the constant is \(\color{red}3\)

  35. anonymous
    • one year ago
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    yeah it is A

  36. lalaland_lauren
    • one year ago
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    so one with no exponent or variable, just a flat out number

  37. anonymous
    • one year ago
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    right called a "constant" because it does not depend of what \(x\) is

  38. anonymous
    • one year ago
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    i have a question do you know what \\[2x^3+5x^2+4x+7\] is if \(x=10\)?

  39. lalaland_lauren
    • one year ago
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    \[2(10)^3+5(10)^2+4(10)+7\] \[2(1,000)+5(100)+40+7\] two thousand five hundred and forty seven

  40. anonymous
    • one year ago
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    right so you see we write our whole numbers as polynomials, using base ten (instead of x)

  41. anonymous
    • one year ago
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    \[2(10)^3+5(10)^2+4(10)+7=2547\]

  42. anonymous
    • one year ago
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    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

  43. lalaland_lauren
    • one year ago
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    okay :-) can you help me with some more questions?

  44. lalaland_lauren
    • one year ago
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    it's like two or three more, one I think I got down

  45. anonymous
    • one year ago
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    sure

  46. lalaland_lauren
    • one year ago
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    4x^2 + 3xy + 12yz this would be a second degree trinomial correct?

  47. anonymous
    • one year ago
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    yes

  48. lalaland_lauren
    • one year ago
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    okay that's what I put, next one

  49. lalaland_lauren
    • one year ago
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    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

  50. lalaland_lauren
    • one year ago
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    Is it C?

  51. lalaland_lauren
    • one year ago
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    Because I think that terms are the sets in the polynomial

  52. anonymous
    • one year ago
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    the "number of terms"? yeah we can count for sure

  53. anonymous
    • one year ago
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    you are right, it is C

  54. lalaland_lauren
    • one year ago
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    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.

  55. lalaland_lauren
    • one year ago
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    I feel like it's C again

  56. anonymous
    • one year ago
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    not this time

  57. anonymous
    • one year ago
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    a polynomial cannot have a variable in the denominator

  58. anonymous
    • one year ago
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    " The expression has a variable raised to a fraction." actually makes no sense at all go with D

  59. lalaland_lauren
    • one year ago
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    oh okay, I thought fractions weren't supposed to be in polynomials period lol

  60. anonymous
    • one year ago
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    unless it means something iike \[x^{\frac{2}{3}}\]which is NOT a polynomial

  61. anonymous
    • one year ago
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    the coeficients can be fractions \[\frac{4}{5}x^2\] is a polynomial

  62. lalaland_lauren
    • one year ago
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    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

  63. anonymous
    • one year ago
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    standard form means order the terms from highest degree to lowest degree

  64. lalaland_lauren
    • one year ago
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    Then D

  65. anonymous
    • one year ago
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    yes

  66. lalaland_lauren
    • one year ago
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    I got a one hundred, thank you so much!!

  67. anonymous
    • one year ago
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    yay yw see you in lala land

  68. lalaland_lauren
    • one year ago
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    Lol! I'll probably need help tomorrow, will you still be on?

  69. anonymous
    • one year ago
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    always glad to help someone who is actually trying

  70. anonymous
    • one year ago
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    probably you can always tag me if you like

  71. lalaland_lauren
    • one year ago
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    Okay :) thank you so much, I have to go to sleep now. Good night!

  72. anonymous
    • one year ago
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    sometime around 9:30 or 10 usually gnight

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