The degree of a polynomial is the highest degree of its monomials with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it. The term order has been used as a synonym of degree but, nowadays, may refer to several other concepts (see order of a polynomial).
A polynomial as oppose to the monomial is a sum of monomials where each monomial is called a term. The degree of the polynomial is the greatest degree of its terms. A polynomial is usually written with the term with the highest exponent of the variable first and then decreasing from left to right.