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Math Help - Dividing Polynomials

  1. #1
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    Dividing Polynomials

    I know how to do the long division method but i'm a bit lost with the synthetic way. What are the rules and method in doing it this way?


    An example to use


    (x^6 + x^4 + x^2 + 1) / (x^2 + 1)



    Thanks alot
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  2. #2
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    Krizalid's Avatar
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    Quote Originally Posted by JonathanEyoon View Post
    (x^6 + x^4 + x^2 + 1) / (x^2 + 1)
    x^6+x^4+x^2+1=x^4(x^2+1)+(x^2+1)

    Does that make sense?
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  3. #3
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    Quote Originally Posted by Krizalid View Post
    x^6+x^4+x^2+1=x^4(x^2+1)+(x^2+1)

    Does that make sense?

    yea but isn't that just factoring out? Or does it have something to do with dividing by means of the synthetic method?
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by JonathanEyoon View Post
    I know how to do the long division method but i'm a bit lost with the synthetic way. What are the rules and method in doing it this way?


    An example to use


    (x^6 + x^4 + x^2 + 1) / (x^2 + 1)



    Thanks alot
    You can't do synthetic division unless you are dividing by a linear polynomial.

    So in this case, let y = x^2. Then you wish to divide y^3 + y^2 + y + 1 by y + 1, which is a problem you can do synthetically:
    Code:
    -1 | 1   1  1   1
       |    -1  0  -1
         1   0  1  |0
    So the result is y^2 + 1 = x^4 + 1.

    -Dan
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  5. #5
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    Thanks alot guys.
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