Trinomial

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:
where
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

Notes

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

References

  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.


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