A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Arrange the following polynomial into descending order for x, then interpret the degree of the 3rd term. 2xyto the power of 4 + 2xto the power of 2y − 3yto the pwer of 2 + 10xto the power of 3

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @ospreytriple

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Is it\[2xy ^{4} + 2x ^{2y} - 3y ^{2} + 10x ^{3}\]

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Or maybe\[2xy ^{4} + 2x ^{2}y - 3y ^{2} + 10x ^{3}\]

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm having difficulty understanding the question. Is the given expression one of the ones I wrote above?

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the seconf one is what they gave me.

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    OK. What the question asks you to do is to arrange the terms of the expression in descending powers of x. Can you do that?

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    nope lol

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No problem. Do you know what a term is? How many terms are there in the given expression?

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    4?

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That's right. Very good. In an algebraic expression, terms are separated by plus and minus signs.

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So for each of the four terms, look at the exponent of x. Arrange the terms from the highest to the lowest exponent of x. What do you think?

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Which term has the highest exponent of x?

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2xy to the power of 4

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Not quite. In\[2xy ^{4}\]the 4 is the exponent of y. The exponent of x is 1. Remember that when there is no numbered exponent, it is assumed to be 1. Make sense?

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So, think of it like\[2x ^{1}y ^{4}\]

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah

  17. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So which term has the highest exponent of x?

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so 3y to the power of 2?

  19. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No. In this term, x doesn't even appear, so it has an exponent of 0. Think of it like\[3x ^{0}y ^{2}\]Try again.

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    10x to 3?

  21. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That's the one. So that term has to come first. Which term comes next?

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3x to 2?

  23. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    There is no such term in the given expression. Look closely.

  24. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh 3y to 2

  25. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    But recall that there is no x, so it's exponent is zero. Think of it like\[3x ^{0}y ^{2}\]For this question, forget about the exponent of y. The y's are just along for the ride. The question asks you to order the terms based on the exponent of the x. That's all.

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    All you should be concerned with is the exponent of the x.

  27. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Let's try looking at it a from a different angle. The first term in the expression is\[2xy ^{4}\]What is the exponent of the x in this term?

  28. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    0

  29. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Nope. Remember when there no numbered exponent, it is assumed to be ...?

  30. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    this is so hard!!!!

  31. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You're doing fine. With some practice, you'll see how easy it is. Any variable (or number) without an exponent written has an exponent of 1. For example\[x=x ^{1}\]\[y=y ^{1}\]\[4=4^{1}\]and so on. If there is no exponent written, it is assumed to be 1. That OK?

  32. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah

  33. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    For another example, in the term\[5xy ^{3}\]the exponent of the 5 is 1 (because there's no written exponent) the exponent of the x is also 1 (because no exponent is written) and the exponent of the y is 3 Get it so far?

  34. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah

  35. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The other rule about exponents that we need for this question is that the value of any number raised to the exponent zero is 1. Mathematically\[x ^{0}=1\]\[y ^{0}=1\]\[2^{0}=1\]. OK?

  36. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay

  37. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Good. We have all the tools we need. So let's look at the first term again\[2xy ^{4}\]What is the exponent of x?

  38. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1

  39. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Bravo! Now you're getting it. The second term is\[2x ^{2}y\]What's the exponent of x?

  40. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2

  41. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yayy! The next term is\[3y ^{2}\]What is the exponent of x? Tricky. Be careful.

  42. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    0

  43. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm so proud of you! And the last term is\[10x ^{3}\]What's the exponent of x?

  44. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    0

  45. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oops. Have another look.

  46. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohh 2

  47. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Almost. Check again.

  48. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3 srry i dont have my contacts in

  49. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    There you go. Now put these four terms in order from the highest exponent of x to the lowest. Don't forget...the sign (+ or -) has to go with the term.

  50. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    10x*3+2xy*4+2x*2y-3y*2

  51. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Close. Check out the second and third terms. Are they in the right order?

  52. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no? swap them

  53. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That's right. 2xy^4 has a x-exponent of 1 while 2x^2y has an x-exponent of 2. Understand?

  54. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah

  55. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok. So re-order those terms and you'll have your answer.

  56. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Want to practice identifying exponents for a couple of minutes to reinforce this?

  57. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the answers are either 1 2 3 or 5

  58. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh. Sorry, you're right. I had to go back and read the original question. So, now that the terms are all in the correct order, the question wants to know what the degree of the third term is. OK. So what is the third term when they're all in order?

  59. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2?

  60. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The whole term?

  61. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    they dont give the whole thing as options just 1 2 3 5

  62. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I know. But we need to examine the whole term to determine what degree it is. So what is the 3rd term?

  63. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2x*2y

  64. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Nope. That's the 2nd term. What's the third?

  65. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2xy*4

  66. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Right on. Do you know what degree means?

  67. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    nope

  68. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It's simple. The degree of an algebraic term is the sum of the exponents of ALL the variables in the term. Can you do that?

  69. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    nope lol

  70. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Add the exponents of the x and y together to get the degree.

  71. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    would it be 3 then?

  72. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    In\[2xy ^{4}\]what is the exponent of the x? what is the exponent of the y? add them together

  73. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    5

  74. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Hooray. The degree of that term is 5. There's your answer.

  75. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    finally thank you!! lol

  76. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You're welcome. Practising identifying the exponents of variables and determining the degree of terms will make it seem much easier.

  77. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Keep up the hard work

  78. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.