degree of a term

The degree of a term measures how “heavy” its variable part is — how many variable factors are multiplied together. A term with one x is degree 1; a term with x times x is degree 2; a plain number, with no variable at all, is degree 0.

When a term has several variables, you add all their exponents. So 5x^3 has degree 3, and 4x^2y has degree 2 + 1 = 3, since the exponent on x is 2 and the (unwritten) exponent on y is 1. The numerical coefficient plays no role at all in the degree — only the exponents of the variables count.

Two cautions. A constant term like 7 has degree 0, because 7 = 7·x^0 and any nonzero number to the zero power is 1. And the number 0 by itself is usually said to have no degree (or undefined degree), a special case worth remembering. The degree of a term feeds into the degree of the whole polynomial.