# Math Help - polynomial?

1. ## 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?

2. Originally Posted by the kopite
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

3. 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.

4. Originally Posted by the kopite
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?

Definition of a rational function

5. ok tx craig that was relatively helpful.

6. Originally Posted by the kopite
ok tx craig that was relatively helpful.

7. 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'.
?

8. Originally Posted by the kopite
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.

9. can i have an example of a non-polynomial then?
thanks for helping clear things up

10. Originally Posted by the kopite
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.