Degree of A Polynomial

Degree Of A Polynomial

The degree of a polynomial is the highest degree of its terms, when the polynomial is expressed in canonical form (i.e. as a linear combination of monomials). The degree of a term is the sum of the exponents of the variables that appear in it. The word degree is now standard, but in some older books, the word order may be used instead.

For example, the polynomial has three terms. (Notice, this polynomial can also be expressed as .) 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 ), one has to put it first in standard form by expanding the products (by distributivity) and combining the like terms; for example, and its degree is 1, although 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.