trinomial

trinomial

A student writes a trinomial on the chalkboard.

Definition

  1. Noun:

    • Mathematics: A "trinomial" is a polynomial consisting of exactly three distinct terms. For example, (x^2 + 3x + 2) is a trinomial because it has three terms separated by plus or minus signs.

  2. Adjective:

    • Mathematics: Pertaining to or having the form of a trinomial. For instance, a "trinomial equation" is an equation that involves a trinomial expression.
Usage Examples

  • Noun:

    • The expression (a^2 + 2ab + b^2) is a perfect square trinomial. (This is a polynomial with three terms that can be factored as ((a+b)^2).)
    • Students learn to factor trinomials in algebra class. (They learn to rewrite a three-term polynomial as a product of two binomials.)

  • Adjective:

    • We solved a trinomial equation by setting it equal to zero. (An equation that contains a trinomial expression.)
    • The teacher explained the trinomial expansion formula. (A formula used to expand expressions like ((x+y)^3) into a trinomial.)
Advanced Usage

  • "Perfect square trinomial": a trinomial that can be written as the square of a binomial (e.g., (x^2 + 6x + 9 = (x+3)^2)).

    • Recognizing a perfect square trinomial simplifies factoring. (It allows you to quickly write the expression as a squared binomial.)

  • "Trinomial cube": a physical model used in Montessori education to represent the algebraic expansion of ((a+b+c)^3).

    • The trinomial cube helps children visualize algebraic relationships. (It is a hands-on learning tool.)
Variants and Related Words
  • Trinomial (adj): used only in mathematical contexts; no common variants.
  • Binomial (n/adj): a polynomial with two terms (related term).
    • A binomial has two terms, while a trinomial has three. (Comparison of polynomial types.)
Synonyms
  • Three-term polynomial: a descriptive phrase for a trinomial.
    • A trinomial is simply a three-term polynomial. (Equivalent in meaning but more verbose.)
Phrasal Verbs
  • None directly applicable; "trinomial" is a technical term and does not form phrasal verbs.
Related Idioms
  • None; "trinomial" is a specialized mathematical term with no idiomatic usage in everyday language.