Definition

1. Adjective:

   • Having the character of a polynomial: Describes an expression or function that is structured as a sum of multiple terms, each consisting of a constant multiplied by one or more variables raised to non-negative integer powers.

2. Noun:

   • A mathematical function that is the sum of a number of terms: A formal sum of terms, each of which is a product of a constant coefficient and one or more variables raised to powers. It is a generalization of a polynomial that may involve multiple variables.

Examples of Usage

• Adjective:

  • The expression 3x²y + 2xy - 7 is a multinomial expression.
  • We simplified the multinomial equation before solving it.

• Noun:

  • The expansion of (x + y + z)³ results in a multinomial with several terms.
  • In algebra, a multinomial can have more than one variable.

Advanced Usage

• "Multinomial Theorem": A theorem that generalizes the binomial theorem, describing the expansion of a power of a sum into a sum of multinomial terms.

  • The Multinomial Theorem is essential for finding coefficients in complex expansions.

• "Multinomial Coefficient": A coefficient that appears in the multinomial theorem, representing the number of ways to partition a set of objects into subsets of specified sizes.

  • Calculate the multinomial coefficient for the term x²y³z in the expansion.

Variants and Related Words

• Polynomial (n/adj): A special case of a multinomial, typically referring to an expression with one variable or used more narrowly in some contexts. While all polynomials are multinomials, not all multinomials are called polynomials in every context.

  • A quadratic equation is a type of polynomial.

• Binomial (n/adj): An expression consisting of exactly two terms.

  • (x + 5) is a simple binomial.

Synonyms

• Polynomial (when used as a noun in a general sense).
• Algebraic expression (a broader, less specific term).

Related Phrases

• "Multinomial distribution": In probability theory and statistics, a generalization of the binomial distribution that describes the outcomes of a multi-category experiment.
  • The multinomial distribution models the probability of counts for rolling a die multiple times.

Related Idioms

(This term is technical and does not have common idiomatic expressions.)

Adjective

1. having the character of a polynomial
   • a polynomial expression

Noun

1. a mathematical function that is the sum of a number of terms