Results 1 to 5 of 5

Math Help - polynomials

  1. March 30th 2009, 02:07 PM #1
    sidi
    sidi is offline
    Junior Member
    Joined
    Mar 2009
    Posts
    44

    polynomials

    I have one more problem...
    I want to find all rings Zn, such the polynomial x+2 divides polynomial (x^5)-10x+12.
    Could anybody help me?
    Thanks, this is a new topic for me...
    Follow Math Help Forum on Facebook and Google+
  2. March 30th 2009, 02:49 PM #2
    NonCommAlg
    NonCommAlg is offline
    MHF Contributor
    Joined
    May 2008
    Posts
    2,296
    Thanks
    7
    Quote Originally Posted by sidi View Post

    I have one more problem...
    I want to find all rings Zn, such the polynomial x+2 divides polynomial (x^5)-10x+12.
    Could anybody help me?
    Thanks, this is a new topic for me...
    x^5 - 10x + 12 is divisible by x+2 in any (unitary) ring because (-2)^5 -10 \times (-2) + 12 = \text{what} ?
    Follow Math Help Forum on Facebook and Google+
  3. March 31st 2009, 03:46 PM #3
    sidi
    sidi is offline
    Junior Member
    Joined
    Mar 2009
    Posts
    44
    of course, -2 is root of that polynomial...I know. I think it should work, that it is divisible in any ring, but I canīt find the reason...
    Zn isnīt a subring of Z, or am I wrong??
    Follow Math Help Forum on Facebook and Google+
  4. March 31st 2009, 04:41 PM #4
    NonCommAlg
    NonCommAlg is offline
    MHF Contributor
    Joined
    May 2008
    Posts
    2,296
    Thanks
    7
    Quote Originally Posted by sidi View Post

    Zn isnīt a subring of Z, or am I wrong??
    no, it's not a subring of Z.
    Follow Math Help Forum on Facebook and Google+
  5. March 31st 2009, 04:53 PM #5
    sidi
    sidi is offline
    Junior Member
    Joined
    Mar 2009
    Posts
    44
    can you give me one more hint please? I am really trying to find out why it is so in any ring, but Iīm afraid Iīm not able to do it now. I have passed an exam (not algebra) few hours ago, Iīm exhausted, but I really want to do my homework...
    Follow Math Help Forum on Facebook and Google+
« Gram-Schmidt process | Bases and transition matrix question »

Similar Math Help Forum Discussions

  1. Roots of 3rd degree polynomials and Characteristic Polynomials
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: April 7th 2011, 01:38 PM
  2. GCD of polynomials in Zn[x]
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: May 18th 2010, 07:22 AM
  3. Polynomials
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 16th 2010, 07:52 AM
  4. Polynomials written as a product of irreducible polynomials
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: January 8th 2010, 04:13 AM
  5. Dividing Polynomials AND Factoring Polynomials
    Posted in the Algebra Forum
    Replies: 5
    Last Post: November 29th 2005, 04:22 PM

Search Tags


/mathhelpforum @mathhelpforum