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Polynomial Degree


The polynomial degree of a nonzero univariate polynomial is its highest power, and is sometimes called its "order." For example, the polynomial

 P(x)=a_nx^n+...+a_2x^2+a_1x+a_0

has degree n if its leading coefficient a_n!=0, denoted degP(x)=n. The (structural) degree of a polynomial is implemented in the Wolfram Language as Exponent[poly, x]. For a polynomial with coefficients that are exact rational numbers, its degree is computable by finding the highest power with a nonzero coefficient. Richardson's theorem instead concerns zero testing for a richer class of elementary functions.


See also

Degree, Leading Coefficient, Polynomial, Polynomial Order, Richardson's Theorem, Total Degree, Univariate Polynomial

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Cite this as:

Weisstein, Eric W. "Polynomial Degree." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PolynomialDegree.html

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