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

- with variables
- with variables
- with variables
- , the quadratic polynomial in standard form with variables.
^{[note 1]} - with variables, nonnegative integers and any constants.
- where is variable and constants are nonnegative integers and any constants.

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]}

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

- where
- For instance, 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 factorization:*x*^{2}+ 3*x*+ 2 = (*x*+*a*_{1})(*x*+*a*_{2}) = (*x*+ 2)(*x*+ 1).

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

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