In elementary algebra, a trinomial is a polynomial consisting of three terms or monomials.
Examples of trinomial expressions with variables with variables with variables , the quadratic polynomial in standard form with variables.Quadratic expressions are not always trinomials, the expressions' appearance can vary. 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.
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
Pascal%27s_pyramid Trinomial expansion Monomial Binomial Multinomial Simple expression Compound expression Sparse polynomial
Notes
References