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

Examples of trinomial expressions

1. variables

2. variables

3. variables

4. , the quadratic polynomial variables.

5. nonnegative integers any constants.

6. any constants.

Trinomial equation

A trinomial equation is a polynomial 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:

  1. .

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

See also

• Pascal%27s_pyramid

• Trinomial expansion

• Monomial

• Binomial

• Multinomial

• Simple expression

• Compound expression

• Sparse polynomial

Notes

References