Polynomial is a mathematical term that refers to an expression consisting of several terms that can be added, subtracted, or multiplied together. The spelling of polynomial can be explained using the International Phonetic Alphabet (IPA) transcription as /ˌpɑːlɪˈnoʊmiəl/. The first syllable, "poli," is pronounced like "polly" with a short "i" sound. The second syllable, "no," is pronounced with a long "o" sound, as in "note." The final syllable, "mial," is pronounced like "meal" with a long "i" sound.
A polynomial is a mathematical expression consisting of one or more terms, with each term comprising a variable raised to a non-negative integer exponent, multiplied by a coefficient. The term "polynomial" is derived from the Latin words "polus" meaning "multiple" and "nomium" meaning "term."
Polynomials are considered algebraic expressions that can involve addition, subtraction, multiplication, and exponentiation operations. The exponents must be whole numbers, ensuring that there are no fractional or negative powers involved. Each term within a polynomial can be represented as the product of a coefficient, which is a constant number, and a variable raised to a power or exponent.
For instance, the polynomial expression "3x^2 + 2xy - 5" consists of three terms. The first term, "3x^2," includes the variable "x" raised to the power of 2, multiplied by the coefficient 3. The second term, "2xy," involves the variables "x" and "y" multiplied by the coefficient 2. Finally, the last term, "-5," is a constant term without any variables.
Polynomials can be classified based on their number of terms. A polynomial with a single term is called a monomial, while a polynomial with two terms is called a binomial. A polynomial with three terms is known as a trinomial, and a polynomial with more than three terms is generally referred to as a polynomial of higher degree.
• An algebraic quantity consisting of many terms.
• Pert. to; containing many terms or many names.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.
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The word "polynomial" has its roots in Greek. It is derived from two Greek words: "poly" which means "many", and "nomial" which comes from "nomos" meaning "law" or "rule". Therefore, "polynomial" can be translated as "many terms" or "many rules". This name accurately reflects the nature of a polynomial, which is an algebraic expression consisting of multiple terms with variables raised to non-negative integer exponents.