Results 1 to 4 of 4

Math Help - Dividing polynomials with a remainder

  1. #1
    Newbie
    Joined
    May 2012
    From
    kanaida
    Posts
    17

    Dividing polynomials with a remainder

    Divide: by


    pllzzzz help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Re: Dividing polynomials with a remainder

    Factorize the numerator!

    By grouping we get

    x^4+x^3y-xy^3-y^4 = x^3(x+y)-y^3(x+y) = (x+y)(x^3-y^3)

    This should get you started. Note the 2nd factor is the difference of cubes and can be factored as well.

    after you have factored both the numerator and denominator the entire denominator should reduce out.

    Try to work this out and post back with your work if you get stuck.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Sep 2012
    From
    Washington DC USA
    Posts
    525
    Thanks
    146

    Re: Dividing polynomials with a remainder

    You can almost do this "by inspection".

    I see (x^4 - y^4), so I see an (x^2 - y^2) in there.

    The rest of the numerator is x^3y-xy^3, which factors into xy(x^2 - y^2).
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,683
    Thanks
    615

    Re: Dividing polynomials with a remainder

    Hello, koolaid123!

    \text{Divide: }\:(x^4+x^3y-xy^3 - y^4) \div (x^2-y^2)

    I don't suppose you tried long division . . .


    \begin{array}{ccccccccccccc} &&&&&& x^2 &+& xy &+&y^2 \\ && --&--&--&--&--&--&--&--&-- \\x^2-y^2 & | & x^4 &+& x^3y && &-& xy^3 & - & y^4 \\ && x^4 && &-& x^2y^2 \\&& --&--&--&--&-- \\ &&&& x^3y &+& x^2y^2 &-& xy^3 \\ &&&& x^3y && &-& xy^3 \\ &&&& --&--&--&--&-- \\ &&&&&& x^2y^2 && &-& y^4 \\ &&&&&& x^2y^2 && &-& y^4 \\ &&&&&& --&--&--&--&-- \end{array}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Remainder when dividing by 49.
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: May 29th 2011, 03:18 PM
  2. Dividing Polynomials: Remainder.
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: September 18th 2010, 05:25 PM
  3. Replies: 2
    Last Post: March 19th 2010, 01:04 PM
  4. dividing remainder w/exponents
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: November 6th 2008, 02:47 PM
  5. Replies: 5
    Last Post: November 29th 2005, 03:22 PM

Search Tags


/mathhelpforum @mathhelpforum