Results 1 to 4 of 4

Math Help - Polynomial problem

  1. #1
    Member
    Joined
    Jan 2009
    From
    London
    Posts
    92

    Polynomial problem

    Hi - I have an assignment with a question that is stumping me at the first hurdle.

    Express x^4 - 4x^2 + 16 in the form
    (x^2 + Ax + B) (x^2 +Cx + D)

    where A,B,C & D are real constants.

    I just can't see how to get it in this form to complete the rest of the partial fraction question. Any ideas??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    It's telling you how to express it?

    To find A, B, C and D you can equate the coefficients
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by dojo View Post
    Hi - I have an assignment with a question that is stumping me at the first hurdle.

    Express x^4 - 4x^2 + 16 in the form

    (x^2 + Ax + B) (x^2 +Cx + D) just multiply this out and compare coefficients

    where A,B,C & D are real constants.

    I just can't see how to get it in this form to complete the rest of the partial fraction question. Any ideas??
    x^4-4x^2+16=\left(x^2+Ax+B\right)\left(x^2+Cx+D\right)

    =x^4+Cx^3+Dx^2+Ax^3+ACx^2+ADx+Bx^2+BCx+BD

    =x^4+x^3(A+C)+x^2(B+AC+D)+x(AD+BC)+BD

    which tells us that A=-C and AD=-BC

    since x^4-4x^2+16 has no x^3 or x terms.

    Also B+AC+D=-4 and BD=16

    from which the values A, B, C, D are discovered.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,048
    Thanks
    1684
    We can rewrite x^4- 4x^2+ 16 as x^4+ 8x^2+ 16- 12x^2= (x^2+ 4)^2- 12x^2 and treat it as a "difference of squares". Of course, it cannot be factored with integer coefficients.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Polynomial problem
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: January 15th 2011, 02:44 AM
  2. problem with polynomial
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 23rd 2010, 05:59 PM
  3. Another polynomial problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 23rd 2009, 06:00 PM
  4. Polynomial problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 3rd 2009, 01:45 PM
  5. A Problem of Polynomial
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 9th 2008, 04:09 AM

/mathhelpforum @mathhelpforum