In elementary algebra, a trinomial is a polynomial consisting of three terms or monomials.[1]

Layers of Pascal's pyramid derived from coefficients in an upside-down ternary plot of the terms in the expansions of the powers of a trinomial

Examples of trinomial expressions

  1.   with   variables
  2.   with   variables
  3.   with   variables
  4.  , the quadratic polynomial in standard form with   variables.[note 1]
  5.   with   variables,   nonnegative integers and   any constants.
  6.   where   is variable and constants   are nonnegative integers and   any constants.

Trinomial equation


A trinomial equation is a polynomial equation involving three terms. An example is the equation   studied by Johann Heinrich Lambert in the 18th century.[2]

Some notable trinomials

  • The quadratic trinomial in standard form (as from above):
  • A special type of trinomial can be factored in a manner similar to quadratics since it can be viewed as a quadratic in a new variable (xn below). This form is factored as:
For instance, the polynomial x2 + 3x + 2 is an example of this type of trinomial with n = 1. The solution a1 = −2 and a2 = −1 of the above system gives the trinomial factorization:
x2 + 3x + 2 = (x + a1)(x + a2) = (x + 2)(x + 1).
The same result can be provided by Ruffini's rule, but with a more complex and time-consuming process.

See also



  1. ^ Quadratic expressions are not always trinomials, the expressions' appearance can vary.


  1. ^ "Definition of Trinomial". Math Is Fun. Retrieved 16 April 2016.
  2. ^ Corless, R. M.; Gonnet, G. H.; Hare, D. E. G.; Jerey, D. J.; Knuth, D. E. (1996). "On the Lambert W Function" (PDF). Advances in Computational Mathematics. 5 (1): 329–359. doi:10.1007/BF02124750.