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

## Trinomial expressions

- with variables
- with variables
- with variables
- with variables, nonnegative integers and any constants.
- 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

- sum or difference of two cubes:

- 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 (
*x*^{n}below). This form is factored as:

where

For example, the polynomial (*x*^{2} + 3*x* + 2) is an example of this type of trinomial with *n* = 1. The solution *a*_{1} = 2 and *a*_{2} = 1 of the above system gives the trinomial factoring:

- (
*x*^{2}+ 3*x*+ 2) = (*x*+*a*_{1})(*x*+*a*_{2}) = (*x*+ 2)(*x*+ 1).

The same result can be provided by the Ruffini's rule, but with a more complex and time-consuming process.

## See also

## References

**^**"Definition of Trinomial".*Math Is Fun*. Retrieved 16 April 2016.**^**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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