1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Factorisation of x^22 -3x^11 +2

  1. Apr 29, 2007 #1
    factorize [tex] x^{22} -3x^{11} + 2 [/tex]

    right so I have p(x) = (x^11 -2)(x^11 - 1)

    (x^11 -2) satifies eisentstein, obviously x-1 is a factor of the second factor. Long division reaps [tex] x^{10} + x^9 +...+x + 1 [/tex]

    the solution asserts that this is also irreducible, but I do not see this?? Is this one of those where you substitue x for y+1??
     
    Last edited: Apr 29, 2007
  2. jcsd
  3. Apr 29, 2007 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Formatting tip: use curly braces {} to group the entire exponent together as one unit.
     
  4. Apr 29, 2007 #3

    StatusX

    User Avatar
    Homework Helper

    Yea, any polynomial of the form (x^p-1)/(x-1) can be shown to be irreducible by making the substitution y=x+1 and applying Eisenstein's criteria. You have to do a little work with binomial coefficients, and it's probably easier to prove this general case then the case p=11.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Factorisation of x^22 -3x^11 +2
  1. Matrix X^2=0 -> Tr(X)=0? (Replies: 10)

  2. Radicals and 2^11-1 (Replies: 5)

  3. (x^2 - y^2) (Replies: 5)

Loading...