A polynomial is a finite sum of terms constructed from variables. Polynomial rules indicate that only addition, subtraction and multiplication operations may be applied, and the integer exponent must be a nonnegative number. The degree of a polynomial is the highest exponent from all its terms. This can easily be confused with the degree of a term, which is the sum of the exponents assigned to each variable in the term.

Read the polynomial. A proper polynomial will have the highest degree first, and it will descend accordingly through the terms. However, not all polynomials are written this way. For example, 5xy^5 + 3x^3 + 5y is a correct polynomial expression, but you may find it written as 3x^3 + 5y + 5xy^5.

Determine which terms in the expression can contain polynomial degrees. In the example 5xy^5 + 3x^3 + 5y, the following have polynomial degrees: 5xy^5  x = 1, y = 5; 3x^3  x = 3; 5y  y = 1.

Take the largest degree from the polynomial. For 5xy^5 + 3x^3 + 5y, the largest degree is 5. This is the degree of the polynomial.
Tips & Warnings
 When looking at the degree of a term, the degrees are added together. For 5xy^5 + 3x^3 + 5y, add the numbers together. The degree of the term for this polynomial is 10: 1 + 5 + 3 + 1.
 Only the variables are added, not the constant term. The coefficient 5 in the 5xy^5 term is a constant. Its degree is a 0, and therefore not counted.
References
 Photo Credit homework image by Galina Barskaya from Fotolia.com