Results 1 to 8 of 8

Math Help - Proving unique factorization for polynomials

  1. #1
    Newbie
    Joined
    Jun 2010
    Posts
    8

    Question Proving unique factorization for polynomials

    Hi!

    I need to prove that unique factorization works for polynomials. I think it might have something to do with the power of the polynomial and the number of roots...the hint in the problem suggested using the Euclidean Algorithm.


    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Start by stating the theorem.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2010
    Posts
    8
    you mean state the euclidean algorithm? It's a way of finding the GCD

    If you have a and b, the process goes
    a = (q1)b + (r1)
    b = (q2)(r1) + (r2)
    r1 = (q3)(r2) + r3

    and keeps going on until the remainder becomes zero
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor chiph588@'s Avatar
    Joined
    Sep 2008
    From
    Champaign, Illinois
    Posts
    1,163
    In general a ring  R is a  \text{UFD}\iff R[x] is a  \text{UFD} .
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jun 2010
    Posts
    8
    The number theory textbook i'm using says nothing about rings...ring R = UFD?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jun 2010
    Posts
    8
    bump bump bmup
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member roninpro's Avatar
    Joined
    Nov 2009
    Posts
    485
    There are two steps that you need to take. First, you need to show that you can factor every polynomial into a product of primes / irreducibles. Then, you need to show that the factorization is unique.

    Can you see how to prove either part?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Jun 2010
    Posts
    8
    @roninpro yea I think i get it..io'llt ry that out and see how it goes.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Unique Factorization Domains
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: November 9th 2011, 05:45 PM
  2. Unique Factorization
    Posted in the Number Theory Forum
    Replies: 31
    Last Post: November 30th 2010, 02:49 PM
  3. primes and unique factorization
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: January 20th 2010, 12:52 PM
  4. Unique Factorization Domains
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: December 18th 2009, 03:52 PM
  5. Unique factorization
    Posted in the Number Theory Forum
    Replies: 8
    Last Post: November 2nd 2006, 09:22 AM

Search Tags


/mathhelpforum @mathhelpforum