Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By HallsofIvy

Math Help - Find gcd

  1. #1
    Newbie
    Joined
    May 2013
    From
    Houston, Tx
    Posts
    2

    Find gcd

    How to find the gcd of f(x)=x2 - x-2 and g(x)= x3-7x+6 in F3[x]. Expressed as a linear combination of f,g.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    822
    Thanks
    209

    Re: Find gcd

    factorize f(x) and g(x) .
    the product of common factors will be the gcd.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2013
    From
    palestine
    Posts
    29
    Thanks
    6

    Re: Find gcd

    hello every one
    Attached Thumbnails Attached Thumbnails Find gcd-22222222222222.jpg  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2013
    From
    Houston, Tx
    Posts
    2

    Re: Find gcd

    Ok, but what throws me off is the F3[x]. I know its (0,1,2), but how to you apply it?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121

    Re: Find gcd

    So we are dealing in modulo 3. The first thing I would do is simplify x^3- 7x+ 6: 7= 1 (mod 3) and 6= 0 (mod 3). So x^3- 7x+ 6= x^2- x= x(x^2- 1)= x(x- 1)(x+ 1) which we could also write as x(x+2)(x+1). To factor x^2- x- 2= x^2+ 2x+ 1 (mod 3), look at the general (x+ a)(x+ b)= x^2+ (a+b)x+ ab. We need to find a and b such that a+ b= 2 (mod 3) and ab= 1 (mod 3). a= b= 1 should be obvious.
    Last edited by HallsofIvy; May 6th 2013 at 05:25 AM.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 9
    Last Post: November 26th 2012, 01:50 PM
  2. Replies: 8
    Last Post: March 22nd 2011, 04:57 PM
  3. Replies: 2
    Last Post: July 5th 2010, 08:48 PM
  4. Replies: 0
    Last Post: June 16th 2009, 12:43 PM
  5. Replies: 2
    Last Post: April 6th 2009, 08:57 PM

Search Tags


/mathhelpforum @mathhelpforum