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Math Help - Monomials and Polynomials

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    Monomials and Polynomials

    I am having a hard time grasping what makes something a monomial and then subsequently a polynomial. I get that division by a variable is not allowed and therefore not a monomial but why is that? I just like to make sense of these things as I find it much easier to retain if I understand something.

    Also, why is something like 3^1/2x not a monomial when a square root of a constant by itself is? How is that any different than any other constant times a variable?

    Thanks for the help.
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    Re: Monomials and Polynomials

    "Mono" means "One", and "Rail" means "Rail"...

    Seriously though, a monomial consists of ONE term, a polynomial consists of MANY terms (as "Poly" means "Many").
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    Re: Monomials and Polynomials

    Quote Originally Posted by SilentEchoes View Post
    I am having a hard time grasping what makes something a monomial and then subsequently a polynomial. I get that division by a variable is not allowed and therefore not a monomial but why is that? I just like to make sense of these things as I find it much easier to retain if I understand something.
    Also, why is something like 3^1/2x not a monomial when a square root of a constant by itself is? How is that any different than any other constant times a variable?
    There is no universal agreement on this. See here.

    However. there is general agreement that \sqrt3~x is a monomial and that \sqrt{3~x} is not a monomial.
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    Re: Monomials and Polynomials

    Okay, well that is what I thought. Makes sense anyways, I guess my book is taking the 3^1/2x is not approach. Thanks for clarifying that it is not a universal agreement.

    Again though, why is dividing by a variable not considered a monomial? What is the thinking behind this concept? (or is that what is not universally agreed upon?)
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    Re: Monomials and Polynomials

    Because the terms "monomial" and "polynomial" are defined to refer exclusively to numbers multiplying the variables to non-negative integer powers.
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    Re: Monomials and Polynomials

    Makes sense, thanks for the clarification.....but a constant by itself is considered a monomial. How does that fall into that definition? (sorry, just trying to understand)
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    Re: Monomials and Polynomials

    Quote Originally Posted by SilentEchoes View Post
    Makes sense, thanks for the clarification.....but a constant by itself is considered a monomial. How does that fall into that definition? (sorry, just trying to understand)
    Zero is a non-negative integer.

    Therefore, \sqrt5~=~\sqrt5~x^0 is a monomial.
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    Re: Monomials and Polynomials

    Okay, I think I got it now. Appreciate the information.
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