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Concept
Trinomial
Summary
In elementary algebra, a trinomial is a polynomial consisting of three terms or monomials.
with variables
with variables
with variables
the quadratic polynomial in standard form with variables.
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.
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 (xn below). This form is factored as:
where
For instance, 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 factorization:
x2 + 3x + 2 = (x + a1)(x + a2) = (x + 2)(x + 1).
The same result can be provided by Ruffini's rule, but with a more complex and time-consuming process.
Official source
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