Results 1 to 2 of 2

Math Help - Polynomials

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    1

    Polynomials

    The polynomial p(x)=x^3+mx^2+nx-56 is exaclty divisible by x-7 and x+2.

    a) Find the values of m and n

    b) Find the third factor

    c) Sketch

    How do I do this? I have no idea...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2007
    Posts
    1,240

    Talking

    Quote Originally Posted by Unwelcome View Post
    The polynomial p(x)=x^3+mx^2+nx-56 is exaclty divisible by x-7 and x+2.
    If they both divide in evenly (and since they don't contain factors of each other), then their product, x^2 - 5x - 14, must also be a factor of x^3 + mx^2 + nx - 56.

    Obviously, the remaining factor of the cubic must be linear, and clearly the leading coefficient of that factor must be "1". So the remaining factor is of the form "x + a".

    Since the constant of the known factor is -14 and the constant of the original polynomial is -56, then you must have (-56)/(-14) = 4, so the remaining factor must be "x + 4".

    Multiply the known factor by the remaining factor, and see what you get for "m" and "n". Sketch the result.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 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. Replies: 7
    Last Post: January 8th 2010, 04:13 AM
  5. Replies: 5
    Last Post: November 29th 2005, 04:22 PM

Search Tags


/mathhelpforum @mathhelpforum