The function f can be the magnitude of the number, or the degree of a polynomial.
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We may speak of the degree of a Diophantine set as being the least degree of a polynomial in an equation defining that set.
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Recall that the degree of a term is the sum of the exponents on variables, and that the degree of a polynomial is the largest degree of any one term.
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A homogeneous polynomial of degree 0 is simply a scalar, while a homogeneous polynomial of degree 1 is a linear functional, also known as a covector.
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Since the degree of a non-zero polynomial is the largest degree of any one term, this polynomial has degree two.
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If the denominator is a 2nd-degree polynomial or a power of such a polynomial, then the numerator is a 1st-degree polynomial.
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Usually, a polynomial of degree n, for n greater than 3, is called a polynomial of degree n, although the phrases quartic polynomial and quintic polynomial are sometimes used.
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Each fraction in the expansion has as its denominator a polynomial function of degree 1 or 2, or some positive integer power of such a polynomial.
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As with other difference formulas, the degree of a Newton's interpolating polynomial can be increased by adding more terms and points without discarding existing ones.