In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer. For a univariate polynomial, the degree of the polynomial is simply the highest exponent occurring in the polynomial.[1] The term order has been used as a synonym of degree but, nowadays, may refer to several other concepts (see Order of a polynomial (disambiguation)).
For example, the polynomial which can also be written as has three terms. 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, such as , one can put it in standard form by expanding the products (by distributivity) and combining the like terms; for example, is of degree 1, even though each summand has degree 2. However, this is not needed when the polynomial is written as a product of polynomials in standard form, because the degree of a product is the sum of the degrees of the factors.
^Gullberg, Jan (1997), Mathematics From the Birth of Numbers, W. W. Norton & Company, p. 128, ISBN 9780393040029
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