If it only has one variable, say , then you 
just find the term with the largest exponent of 
, considering the constant term to be
multiplied by .  That largest exponent
IS the degree.

 is a polynomial of degree 8

 is a polynomial of degree 1 because  means 

 is also a polynomial of degree 1 because  means 

 is a polynomial of degree 0 because 1 means 

If there are two or more variables, then in the terms with more
than one variable, you add the exponents and the degree of the
polynomial is the largest exponent or sum of exponents:

 has degree 9, because the 
exponents of the term  is 9 because it means  
and adding exponents 

 has degree 3 because  means  and 
adding exponents gives 1+1+1=3.

Edwin