This article is about mathematics. For the use in taxonomy, see Trinomial name. For the use identifying archaeological sites in the United States, see Smithsonian trinomial.

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

Trinomial expressions

1. with variables
2. with variables
3. with variables
4. with variables, nonnegative integers and any constants.
5. 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 (xⁿ below). This form is factored as:

where

For example, 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 factoring:

(x² + 3x+ 2) = (x + a₁)(x + a₂) = (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

• Trinomial expansion
• Monomial
• Binomial
• Multinomial
• Simple expression
• Compound expression

References