Results 1 to 2 of 2

Math Help - [SOLVED] Polynomial division

  1. #1
    Senior Member Spec's Avatar
    Joined
    Aug 2007
    Posts
    318

    [SOLVED] Polynomial division

    Not really a homework question, but I have a test tomorrow and I need to be able to solve these kind of problems.

    Find the remainder when the polynomial x^{100} + x^{67} - x^{32} - 2x^9 +1 is divided with:

    a) x - 1
    b) x + 2
    c) x^2 - x

    I already have the answers, what I'm looking for is how to solve the problems. Polynomial long division would easily fill up several pages, so I'm clueless as what to do.

    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Spec View Post
    Not really a homework question, but I have a test tomorrow and I need to be able to solve these kind of problems.

    Find the remainder when the polynomial x^{100} + x^{67} - x^{32} - 2x^9 +1 is divided with:

    a) x - 1
    b) x + 2
    c) x^2 - x
    !
    Theorem: Given f(x),g(x) two polynomials over \mathbb{Z} with g(x)\not = 0 then f(x) =q(x)g(x)+r(x) and \deg r(x) < \deg g(x) \mbox{ or }r(x)=0.

    So,
    x^{100} + x^{67} - x^{32} - 2x^9 +1=q(x)(x-1)+k.
    It is a constant since the degree is zero.
    Since the above statement is true for all x let x=1 to get:
    0=q(1)(0)+k\implies k=0.
    Thus there is no remainder.

    Try the same approach to the other ones.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Complex Polynomial Division
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: January 25th 2010, 07:09 PM
  2. [SOLVED] polynomial division
    Posted in the Algebra Forum
    Replies: 5
    Last Post: August 9th 2009, 09:17 PM
  3. Polynomial division vs synthetic division
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 9th 2009, 05:49 AM
  4. polynomial division
    Posted in the Algebra Forum
    Replies: 6
    Last Post: November 13th 2008, 04:02 AM
  5. [SOLVED] [SOLVED] need help solving polynomial long division
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 19th 2007, 11:00 PM

Search Tags


/mathhelpforum @mathhelpforum