this site gives a good explanation.
http://www.purplemath.com/modules/polydefs.htm
basically, in a regular polynomial the exponents must be whole numbers
since 3/x^4 = 3x^-4 , this violates that definition
How come x^4/3 is a ploynomial, but 3/x^4 isn't?
2 answers
x cannot have a negative power in a polynomial by definition.
http://www.merriam-webster.com/dictionary/polynomial
http://www.merriam-webster.com/dictionary/polynomial