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Math Help - polynomial?

  1. #1
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    Angry polynomial?

    i am told in my math book that 'a rational function is one where both numerator and denominator are polynomial'
    as an example i am given such functions as '1/x' or '3x+1/x'
    but neither x nor 1 are polynomials, what is this?? or are they just 'zero degree' polynomials? then they are not polynomials, they are monomials, and what is the relevance of the definition in that case?
    Last edited by mr fantastic; May 29th 2009 at 05:09 AM. Reason: Deleted suggestion of bad language
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  2. #2
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    Quote Originally Posted by the kopite View Post
    i am told in my math book that 'a rational function is one where both numerator and denominator are polynomial'
    as an example i am given such functions as '1/x' or '3x+1/x'
    but neither x nor 1 are polynomials, what is this ?? or are they just 'zero degree' polynomials? then they are not polynomials, they are monomials, and what is the relevance of the definition in that case?
    Not sure how to reply other than 1 and x are polynomials. Check out the definition of a polynomial and you'll see that they fit it

    Polynomial -- from Wolfram MathWorld
    Last edited by mr fantastic; May 29th 2009 at 05:41 AM. Reason: Edited quote.
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  3. #3
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    so in theory every monomial is a potential polynomial? every monomial is polynomial? is that correct? thats all i need to know. why does the term monomial exist then? seems pretty superfluous to me.
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  4. #4
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    Quote Originally Posted by the kopite View Post
    i am told in my math book that 'a rational function is one where both numerator and denominator are polynomial'
    as an example i am given such functions as '1/x' or '3x+1/x'
    but neither x nor 1 are polynomials, what is this ?? or are they just 'zero degree' polynomials? then they are not polynomials, they are monomials, and what is the relevance of the definition in that case?
    Maybe this link will help

    Definition of a rational function
    Last edited by mr fantastic; May 29th 2009 at 05:42 AM. Reason: Edited quote.
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  5. #5
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    ok tx craig that was relatively helpful.
    Last edited by mr fantastic; May 29th 2009 at 05:10 AM. Reason: Deleted suggestin of bad language. Deleted off-topic chat.
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  6. #6
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    Quote Originally Posted by the kopite View Post
    ok tx craig that was relatively helpful.
    Glad it helped
    Last edited by mr fantastic; May 29th 2009 at 05:10 AM.
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  7. #7
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    but, finally, as abovementioned, can somebody answer this question:
    is every monomial in essence a polynomial? potentially? because if the simplest units such as 1 and x are in fact polynomials, i really dont see which units can be excluded from this set as being 'monomials and not polynomials'.
    ?
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  8. #8
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    Quote Originally Posted by the kopite View Post
    but, finally, as abovementioned, can somebody answer this question:
    is every monomial in essence a polynomial? potentially? because if the simplest units such as 1 and x are in fact polynomials, i really dont see which units can be excluded from this set as being 'monomials and not polynomials'.
    ?
    A monomial is a particular type of polynomial. Just like a square is a particular type of rectangle.
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  9. #9
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    can i have an example of a non-polynomial then?
    thanks for helping clear things up
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  10. #10
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    Quote Originally Posted by the kopite View Post
    can i have an example of a non-polynomial then?
    thanks for helping clear things up
    Anything that's not a polynomial! Square root functions such as \sqrt{x}, exponential functions, trigonometic functions, logarithmic functions etc. etc.
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