poly·​no·​mi·​al | \ ˌpä-lə-ˈnō-mē-əl How to pronounce polynomial (audio) \

Definition of polynomial

 (Entry 1 of 2)

: a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power (such as a + bx + cx2)



Definition of polynomial (Entry 2 of 2)

: relating to, composed of, or expressed as one or more polynomials polynomial functions polynomial equations

Examples of polynomial in a Sentence

Recent Examples on the Web: Noun Consequently, these three rearrangements are considered to be the symmetries of the polynomial. Quanta Magazine, 3 Aug. 2021 The search for a cubic polynomial with integer coefficients that has three non-real roots will teach you about the importance of complex conjugates — pairs of complex numbers whose product and sum are always real. Quanta Magazine, 18 Nov. 2020 There are different ways to establish the impossibility of this polynomial. Quanta Magazine, 18 Nov. 2020 For example, these conditions violate the rational root theorem, which says that any rational roots of a polynomial must be a ratio of a factor of the constant term divided by a factor of the leading coefficient. Quanta Magazine, 18 Nov. 2020 To pull the phosphine signal out of a messy data set, the team subtracted the background noise using a high-order polynomial, which means more variables were used to model the data than is typical. Nadia Drake, National Geographic, 23 Oct. 2020 Similarly, that team reported that high-order polynomial fitting could create multiple spurious spectral lines. Nadia Drake, National Geographic, 23 Oct. 2020 But x³ − 2 is a degree-three polynomial, so () is not constructible. Quanta Magazine, 14 Sep. 2020 But this polynomial conveys a lot of information about our problem. Quanta Magazine, 13 Aug. 2019 Recent Examples on the Web: Adjective Over the next millennium, algebra evolved from the study of the nature of solutions to polynomial equations to the study of abstract number systems. Emily Riehl, Scientific American, 17 Sep. 2021 Galois groups provide a powerful perspective from which to study polynomial equations. Quanta Magazine, 3 Aug. 2021 The Langlands program is a sprawling research vision that begins with a simple concern: finding solutions to polynomial equations like x2 − 2 = 0 and x4 − 10x2 + 22 = 0. Quanta Magazine, 19 July 2021 In fact it’s an NP-hard problem, where NP stands for non-deterministic polynomial time. Calum Chace, Forbes, 27 May 2021 The exhibit features a wealth of previously unpublished work: printouts of experiments on polynomial equations, found images such as magazine ads and photographs that reminded Mandelbrot of fractals as well as drawings from other mathematicians. Marissa Fessenden, Scientific American, 21 Dec. 2012 Using a technique called polynomial fitting, the original discovery team looked for phosphine’s spectral line by mathematically removing background noise around the region in the spectrum where phosphine should be. Nadia Drake, National Geographic, 23 Oct. 2020 For example, mathematicians would like to know when polynomial equations like 3x3 + 4y3 + 5z3 = 0 have rational solutions. Quanta Magazine, 19 Oct. 2020 In the cube doubling problem, for example, the side length of a cube with twice the volume of the unit cube is , which is a root of the polynomial x³ − 2 because ()³ − 2 = 0. Quanta Magazine, 14 Sep. 2020

These example sentences are selected automatically from various online news sources to reflect current usage of the word 'polynomial.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

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First Known Use of polynomial


1674, in the meaning defined above


circa 1704, in the meaning defined above

History and Etymology for polynomial


poly- + -nomial (as in binomial)

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Time Traveler for polynomial

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The first known use of polynomial was in 1674

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Last Updated

14 Aug 2021

Cite this Entry

“Polynomial.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/polynomial. Accessed 24 Sep. 2021.

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More from Merriam-Webster on polynomial

Britannica.com: Encyclopedia article about polynomial


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