Results 1 to 2 of 2

Math Help - Prove that deg(f(x)g(x))=deg(f(x))+deg(g(x))

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    23

    Prove that deg(f(x)g(x))=deg(f(x))+deg(g(x))

    a.) Let R be an integral domain and f(x), g(x) are elements of R[x]. Prove that deg(f(x)g(x))=deg(f(x))+deg(g(x)).

    b.) Is part (a) true if R is not an integral domain?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by Slazenger3 View Post

    a.) Let R be an integral domain and f(x), g(x) are elements of R[x]. Prove that deg(f(x)g(x))=deg(f(x))+deg(g(x)).

    b.) Is part (a) true if R is not an integral domain?
    a) let f(x)=\sum_{i=0}^n a_ix^i, \ g(x)=\sum_{i=0}^m b_ix^i, \ a_n \neq 0, \ b_m \neq 0. then the leading term of f(x)g(x) is a_nb_mx^{n+m} and a_nb_m \neq 0, because a_n \neq 0, \ b_m \neq 0 and R is an integral domain.

    b) no! a counter-example: R=\mathbb{Z}/4\mathbb{Z}, \ f(x)=g(x)=\bar{2}x.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove a/b and a/c then a/ (3b-7c)
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 23rd 2010, 06:20 PM
  2. prove,,,
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 1st 2010, 10:02 AM
  3. Prove |w + z| <= |w| +|z|
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 28th 2010, 06:44 AM
  4. Replies: 2
    Last Post: August 28th 2009, 03:59 AM
  5. How to prove that n^2 + n + 2 is even??
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 30th 2008, 02:24 PM

Search Tags


/mathhelpforum @mathhelpforum