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Math Help - Help in polynomial division

  1. #1
    Newbie findmehere.genius's Avatar
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    Help in polynomial division

    Hello , i am posting anything here for first time.....I am from India, and in XIth Standard presently.

    I do have some trouble in division of polynomial by another polynomial but without using long division method and application of formula:
    (polynomial in any variable)=(divisor*Q)+remainder; here remainder varies according to degree of polynomial eg. ax+b, ax^2+bx+c, etc.

    Suppose a question is to find the remainder with given polynomial: x^3+x^2-3x-2 with divisor x^2+3x+2;

    I am not able to do it in short cut method.....Pls if any one have idea aout shorter methods...DO REPLY
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by findmehere.genius View Post
    Hello , i am posting anything here for first time.....I am from India, and in XIth Standard presently.

    I do have some trouble in division of polynomial by another polynomial but without using long division method and application of formula:
    (polynomial in any variable)=(divisor*Q)+remainder; here remainder varies according to degree of polynomial eg. ax+b, ax^2+bx+c, etc.

    Suppose a question is to find the remainder with given polynomial: x^3+x^2-3x-2 with divisor x^2+3x+2;

    I am not able to do it in short cut method.....Pls if any one have idea about shorter methods...DO REPLY
    This link might help you though I suggest you to practice thoroughly the method you find as easiest. ...

    Ruffini's rule - Wikipedia, the free encyclopedia
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  3. #3
    MHF Contributor
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    Hi

    x^3+x^2-3x-2 = (x^2+3x+2)P(x) + Q(x)

    deg(P) = deg(x^3+x^2-3x-2) - deg(x^2+3x+2) = 3 - 2 = 1
    deg(Q) < deg(x^2+3x+2)

    x^3+x^2-3x-2 = (x^2+3x+2)(ax+b) + cx+d

    Expand
    x^3+x^2-3x-2= ax^3 + (3a+b)x^2 + (2a+3b+c)x + 2b+d

    Therefore
    a=1
    3a+b=1
    2a+3b+c=-3
    2b+d=-2

    Which leads to
    a=1
    b=-2
    c=1
    d=2

    x^3+x^2-3x-2 = (x^2+3x+2)(x-2) + x+2
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  4. #4
    Newbie findmehere.genius's Avatar
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    Question

    Thanks to both of you who answered my post.
    and Ruffini's rule is somewhat very similar to the the complete division method..
    actually my teacher said that a polinomial is sum of product of divisor and quotient and of remainder...ok that was clear to me.

    He said that in the question we dont have to deal with the quotient so
    the polynomial x^3+x^2-3x-2 = {x^2+3x+2*Q(uotient)}+ax^2+bx+c where ax^2+bx+c is remainder.
    He said to use the hit and trial method to get a value for x that gives value 0 to the equation x^2+3x+2.........such that we put the same value of x in polynomial to be divided and equate the polynomial and remainder........and sorry because I myself am confused in the same......one thing that I can tell that is ax^2+bx+c is remainder and it was solved simultaneously for different value of x.
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