polynomial

From poly- +‎ -nomial, from νομός (nomós, “portion, part”), by analogy with binomial.

• (UK) IPA^(key): /ˌpɒlɪˈnəʊmɪəl/

• Audio (Southern England):

  (file)

• (US) IPA^(key): /ˌpɑliˈnoʊmiəl/

polynomial (plural polynomials)

1. (algebra, strict sense) An expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power, such as ${\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{0}x^{0}}$.
   • 1999, William Dunham, Euler: The Master of Us All, Mathematical Association of America, published 1999, page 116:

     Unfortunately, an analogous attack on the octic polynomial becomes exceedingly complicated.

   • 2016, Grigoriy Blekherman, Daniel Plaumann, Rainer Sinn, Cynthia Vinzant, “Low-Rank Sum-of-Squares Representations on Varieties of Minimal Degree”, in arXiv‎^[1]:

     Our upper bound is the best possible, and it implies the existence of low-rank factorizations of positive semidefinite bivariate matrix polynomials and representations of biforms as sums of few squares.

2. (taxonomy) A taxonomic designation (such as of a subspecies) consisting of more than two terms.

• binomial
• homogeneous polynomial
• monomial
• trinomial
• quadrinomial
• quantic

• rational function

polynomial (not comparable)

1. (algebra) Able to be described or limited by a polynomial.
2. (taxonomy) Of a polynomial name or entity.

• Appendix:English polynomial degrees

• Audio:

  (file)

polynomial (feminine polynomiale, masculine plural polynomiaux, feminine plural polynomiales)

1. polynomial

• polynôme