Results 1 to 7 of 7
Like Tree1Thanks
  • 1 Post By BobP

Math Help - organize polynomial criteria?

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    8

    organize polynomial criteria?

    I'm dividing polynomials, operations like: a^{2}-b^{2}+2bc-c^{2}\div a+b-c
    I know that I can organize first the polynomial in decreasing order for one letter by taking the biggest exponent of that letter and reorganizing form biggest exponent for that letter to lowest. But how can I do with the polynomial I just wrote? What's the criteria? For example for this case, I can organize decreasingly for the variable b, and I get up to this point in the reorganizing process: -b^{2}+2bc... but now the exponent for b is zero for both the terms, a^{2} and -c^{2}
    Which one should be put first in these situations?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    Posts
    660
    Thanks
    133

    Re: organize polynomial criteria?

    Are you sure that you are meant to deal with it that way ? I suspect that you are meant to factorise the top line.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    Posts
    8

    Re: organize polynomial criteria?

    Let me put it in a different way, since unfortunately some words that I use are being translated and perhaps incorrectly used in English. If I have for example 2a^{3}+9a^{4}-14a^{2} and it's the dividend in a division problem, I can put the polynomial in order: here I'd get: 9a^{4}+2a^{3}-14a^{2} The exponents go downwards from the term with the highest degree to the term with the lowest one. How can I do the same for the polynomial that I wrote: a^{2}-b^{2}+2bc-c^{2}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jun 2009
    Posts
    660
    Thanks
    133

    Re: organize polynomial criteria?

    This is a strange operation to want to carry out, but if that's what's required then you have three options.

    Write the dividend as a^{2} - b^{2} + 2bc - c^{2} and divide by a+b-c.

    Write the dividend as -b^{2}+2bc-c^{2}+a^{2} and divide by b-c+a.

    Or, write the dividend as -c^{2}+2bc - b^{2} +a^{2} and divide by -c+b+a.

    The easiest way of dealing with your particular example though is to factorise the top line.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2010
    Posts
    8

    Re: organize polynomial criteria?

    I tried to understand what you meant by factorizing the top line but I still can't see how I could do that...
    When I factorize I'm converting the dividend polynomial into a product. But then I don't see any simplification with the divisor.
    I add the following two images to the question, where I show in orange rectangles, both the same problem. How does one decides to put those spaces to separate the terms in the dividend?
    organize polynomial criteria?-.png
    organize polynomial criteria?-b.png
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Jun 2009
    Posts
    660
    Thanks
    133

    Re: organize polynomial criteria?

    a^{2}-b^{2}+2bc-c^{2}=a^{2}-(b^{2}-2bc+c^{2})=a^{2}-(b-c)^{2}

    =(a-(b-c))(a+(b-c))=(a-b+c)(a+b-c),

    and the a+b-c cancels.

    If the numerator did not contain a+b-c as a factor, division would lead to a remainder.

    As to division, you have to decide on which variable you are dividing wrt and arrange for terms in that variable to occur in descending order. The order of the constant terms will not matter.
    Thanks from querti09
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jul 2010
    Posts
    8

    Re: organize polynomial criteria?

    Thanks BobP for the help, I was struggling by doing (a+b)(a-b)+c(2b-c) with the dividend but now I see it wasn't the right way of dealing with it!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Primality Criteria for F_n(2336)
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: March 21st 2012, 07:36 AM
  2. Bing metrization criteria
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: February 18th 2011, 08:42 PM
  3. Fermats criteria - Correct?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 15th 2008, 08:06 AM
  4. proof of raabe criteria.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 26th 2006, 12:37 PM

Search Tags


/mathhelpforum @mathhelpforum