Results 1 to 2 of 2

Math Help - Find all polynomials p(x)

  1. #1
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Find all polynomials p(x)

    can anybody help me solve in this please.

    Find all polynomials p(x) where xp(x-1) = (x-5)p(x) and p(6) = 5 factorial
    Last edited by rcs; December 19th 2010 at 07:19 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,400
    Thanks
    1848
    Note that, taking x= 5 in the first equation, 5p(4)= 0 which means that p(x) must have a factor of the form x- 4. Write p(x)= (x- 4)q(x) and the first equation becomes xp(x- 1)= x(x- 1- 4)q(x- 1)= x(x- 5)q(x-1)= (x- 5)(x- 4)q(x)) or xq(x-1)= (x- 4)q(x).

    Taking x= 4 in that says that 4q(3)= 0 so that q has a factor of x- 3. Write q(x)= (x- 3)r(x) and xq(x-1)= (x-4)q(x) becomes x(x-1-3)r(x-1)= x(x- 4)r(x-1)= (x-4)(x-3)r(x) so xr(x-1)= (x- 3)r(x).

    Get the point? Keep going and you eventually get to xy(x-1)= xy(x) so that y(x- 1)= y(x) for y a polynomial. That is only possible if y is a constant. If that "!" in p(6)= 5! is a factorial rather than punctuation, it is particularly easy to find that constant.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the Taylor polynomials
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 19th 2011, 07:38 AM
  2. Find the polynomials p (x)
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: January 15th 2011, 02:29 AM
  3. How does one find a basis for a set of polynomials?
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 23rd 2010, 12:19 PM
  4. How do I find the sum of polynomials?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 26th 2009, 07:35 AM
  5. Find the sum of polynomials
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 16th 2007, 03:38 AM

Search Tags


/mathhelpforum @mathhelpforum