Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

frx Group Title

Show that if r is a positive odd integer then the polynomial \[x ^{r}+1\] is dividable by \[x+1\]

  • one year ago
  • one year ago

  • This Question is Closed
  1. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Let f(x)=x^r +1 Now, use remainder theorem

    • one year ago
  2. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Can u?

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

    Don't know the remainder theorem :/

    • one year ago
  4. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    If a polynomial f(x) is divided by (x-a) then (x-a) is a factor of f(x) if f(a)=0.

    • one year ago
  5. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh sorry... it is Factor Theorem.... Now use this factor theorem.

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

    I do get the factor theorem, so that proves a part of it. I do have the answer though and it says that this it only valid if and only if (-1)^r+1=0, what's the meaning of that?

    • one year ago
  7. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    f(x)=x^r +1 Now, when f(x) id divided by (x+1) then, Remainder = f(-1)=(-1)^r+1 Since r is odd (-1)^r=-1 So, Remainder =f(-1)=-1+1=0 Thus,x^r +1 is divisible by x+1

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

    Oh, how stupid, I see that it's just a continuation of the factor theorm, thank you :)

    • one year ago
  9. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Welcome

    • one year ago
    • Attachments:

See more questions >>>

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.