Results 1 to 2 of 2

Math Help - irreducible polynomials

  1. #1
    Junior Member
    Joined
    Apr 2008
    From
    Gainesville
    Posts
    68

    irreducible polynomials

    For polynomials over a field F, prove that every non constant polynomials can be expressed as a product of irreducible polynomials.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by JCIR View Post
    For polynomials over a field F, prove that every non constant polynomials can be expressed as a product of irreducible polynomials.
    If f(x) is irreducible the proof is complete. Otherwise f(x) = p_1(x)p_2(x) where p_1(x),p_2(x) are not constant. If these two polynomials are irreducible the proof is complete. Otherwise keep on going. Eventually you end up with only irreducible polynomials. Because the sums of the degrees need to add up to \deg f(x) and this means you cannot do this indefinitely.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Irreducible Polynomials
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 18th 2011, 02:11 AM
  2. Irreducible Polynomials f(x) = x^7 - x
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: July 24th 2011, 11:47 PM
  3. Irreducible polynomials
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 23rd 2011, 02:07 PM
  4. Replies: 7
    Last Post: January 8th 2010, 04:13 AM
  5. Irreducible polynomials over Q
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: May 23rd 2009, 11:18 PM

Search Tags


/mathhelpforum @mathhelpforum