Name and define the two ways to classify polynomials

The 2 ways a polynomial can be classified is by its degree or by its number of terms.
Number of terms is each amount of individual term. A term is just a number and a variable (possibly to a power/degree). Terms are also separated using a function such as multiplication, addition, and subtraction.

The degree of a polynomial is just the greatest variable's power so if x^5 is the greatest power in that function, than that is the degree of the polynomial 

It will be a whole number.