Results 1 to 2 of 2

Math Help - factor theorem

  1. #1
    Junior Member
    Joined
    Dec 2006
    Posts
    60

    factor theorem

    find the quadratic factor by the method of comparing coefficients for g(x) = x^3 - 2x^2 - 5x + 6. i already found out that the linear factor is (x+2) if that helps.

    i know how to figure it out using long division
    but not by this method
    so could anyone help me? thanks :]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by checkmarks View Post
    find the quadratic factor by the method of comparing coefficients for g(x) = x^3 - 2x^2 - 5x + 6. i already found out that the linear factor is (x+2) if that helps.

    i know how to figure it out using long division
    but not by this method
    so could anyone help me? thanks :]
    You write:

    x^3 - 2x^2 - 5x + 6 = (x+2)(ax^2 + bx + c)

    Multiply out the Right Hand Side:

    x^3 - 2x^2 - 5x + 6 = a x^3 + x^2 (2 a + b) + x (2b + c) + 2c

    So the coefficients of x^3, x^2, x, and the constant terms must be equal, so:

    from the first and last terms:

    a=1, c=3,

    and from the term in x we have:

    2b+c = -5,

    or 2b= -8, so b=-4, and:


    x^3 - 2x^2 - 5x + 6 = (x+2)(x^2 - 4x + 3)

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help on factor theorem.
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 10th 2010, 02:35 AM
  2. Need help on factor theorem.
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 9th 2010, 06:07 PM
  3. factor theorem
    Posted in the Algebra Forum
    Replies: 8
    Last Post: January 5th 2009, 07:43 PM
  4. Factor theorem!
    Posted in the Algebra Forum
    Replies: 4
    Last Post: February 16th 2008, 05:16 AM
  5. Factor Theorem and Remainder Theorem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 8th 2007, 11:50 AM

Search Tags


/mathhelpforum @mathhelpforum