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Math Help - Greatest common divisor

  1. #1
    Senior Member chella182's Avatar
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    Greatest common divisor

    f(X)=X^4+X^3+2X+2 and g(X)=X^3+X^2+X+1.
    f(X) and g(X) are both polynomials over \mathbb{Z}_5. Compute their greatest common divisor.

    My notes aren't helping me here; never done an example like this before, so a detailed explanation of the method would be greatly appreciated
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    Quote Originally Posted by chella182 View Post
    f(X)=X^4+X^3+2X+2 and g(X)=X^3+X^2+X+1.
    f(X) and g(X) are both polynomials over \mathbb{Z}_5. Compute their greatest common divisor.

    My notes aren't helping me here; never done an example like this before, so a detailed explanation of the method would be greatly appreciated
    I'd start by factorising the two functions. To do this bracket the first 2 terms and the last two terms, and proceed to factorise.
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  3. #3
    Senior Member chella182's Avatar
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    Quote Originally Posted by Debsta View Post
    I'd start by factorising the two functions. To do this bracket the first 2 terms and the last two terms, and proceed to factorise.
    I've never heard of that method of factorising... care to explain it?
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    Quote Originally Posted by chella182 View Post
    I've never heard of that method of factorising... care to explain it?
    Doesn't always work but is a method to try when you have 4 terms (it does help in both your cases)
    eg
     x^4+x^3+2x+2 <br />
= (x^4+x^3) + (2x+2)<br />
= x^3(x+1) + 2(x+1)<br />
= (x+1) (x^3+2)<br />
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  5. #5
    Senior Member chella182's Avatar
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    Quote Originally Posted by Debsta View Post
    Doesn't always work but is a method to try when you have 4 terms (it does help in both your cases)
    eg
     x^4+x^3+2x+2 <br />
= (x^4+x^3) + (2x+2)<br />
= x^3(x+1) + 2(x+1)<br />
= (x+1) (x^3+2)<br />
    Wow, thanks! Not sure if my lecturer will appreciate the method if it doesn't always work (he's like that), but it's worth a shot anyway!
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