What is "degree of a polynomial"

n. the degree of the term in the polynomial that has the highest degree

The degree of a polynomial is the highest degree of its terms when the polynomial is expressed in its canonical form consisting of a linear combination of monomials. 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). For example, the polynomial 7xy + 4x − 9 has three terms. (Notice, this polynomial can also be expressed as 7xy + 4xy − 9xy.) The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5 which is the highest degree of any term.

To determine the degree of a polynomial that is not in standard form (for example (x + 1) − (x − 1)), one has to put it first in standard form by expanding the products (by distributivity) and combining the like terms; for example (x + 1) − (x − 1) = 4x is of degree 1, even though each summand has degree 2. However, this is not needed when the polynomial is expressed as a product of polynomials in standard form, because the degree of a product is the sum of the degrees of the factors.