Trinomial

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

Examples of trinomial expressions

1. with variables
2. with variables
3. with variables
4. , the quadratic polynomial in standard form with variables.
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.

Some notable trinomials

• The quadratic trinomial in standard form (as from above):

:

• 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 ( below). This form is factored as:

:

where

:

For instance, the polynomial is an example of this type of trinomial with . The solution and of the above system gives the trinomial factorization:

:.

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

See also

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

Notes

References