Results 1 to 3 of 3

Math Help - polynom remainder

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    1

    polynom remainder

    I get nowhere with problems of the type
    p(x) gives the remainder 3 when divided by (x+3), and the remainder 4 when divided by (x-6). What is the remainder when p(x) is divided by (x+3)(x-6)?

    they say it's related to the factor theorem, but i don't make the connection..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by ferreus View Post
    I get nowhere with problems of the type
    p(x) gives the remainder 3 when divided by (x+3), and the remainder 4 when divided by (x-6). What is the remainder when p(x) is divided by (x+3)(x-6)?

    they say it's related to the factor theorem, but i don't make the connection..
    I'd say that this is a case of the chinese remainder theorem for a polynomial ring.

    You're told that p(x) = q(x)(x+3)+3 and p(x) = r(x)(x-6)+4, for some polynomials q(x), r(x). Multiply the first of those equations by x6 and the second one by x+3, and subtract. You'll get -9p(x) = s(x)(x+3)(x-6) + 3(x-6) - 4(x+3), for some polynomial s(x). Divide by 9 to find the remainder when p(x) is divided by (x+3)(x-6).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Shanks's Avatar
    Joined
    Nov 2009
    From
    BeiJing
    Posts
    374

    solve it by using the factor theorem

    By the factor theoem : let p(x)=q(x)(x+3)(x-6)+ax+b,where q(x) be the quotient, a and b be undetermined coefficients.
    since it leaves a remainder of 3 when divided by x+3, and a remainder of 4 when divided by x-6,we have :
    p(-3)= b -3a = 3 and p(6)= b + 6a = 4
    thus: a = 1/9, b =10/3.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. factorising a polynom with it's roots
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: December 8th 2010, 04:26 AM
  2. complex polynom
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 18th 2010, 01:11 PM
  3. Remainder?
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: October 26th 2009, 10:49 AM
  4. Polynom with real coeff
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: July 2nd 2009, 07:06 AM
  5. Polynom over finite field
    Posted in the Advanced Algebra Forum
    Replies: 14
    Last Post: May 14th 2008, 07:21 AM

Search Tags


/mathhelpforum @mathhelpforum