In
elementary algebra
Elementary algebra encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, whilst algebra introduces variables (quantities without fixed values).
This use of variables entail ...
, a trinomial is a
polynomial
In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...
consisting of three terms or
monomial
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered:
# A monomial, also called power product, is a product of powers of variables with nonnegative integer expone ...
s.
Examples of trinomial expressions
#
with
variables
#
with
variables
#
with
variables
#
, the
quadratic expression in standard form with
variables.
#
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
Johann Heinrich Lambert (, ''Jean-Henri Lambert'' in French; 26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of Mulhouse, generally referred to as either Swiss or French, who made important contributions to the subject ...
in the 18th century.
Some notable trinomials
* The quadratic trinomial in standard form (as from above):
See also
*
Trinomial expansion
In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by
:(a+b+c)^n = \sum_ \, a^i \, b^ \;\! c^k,
where is a nonnegative integer and the sum is taken over all combina ...
*
Monomial
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered:
# A monomial, also called power product, is a product of powers of variables with nonnegative integer expone ...
*
Binomial
Binomial may refer to:
In mathematics
*Binomial (polynomial), a polynomial with two terms
* Binomial coefficient, numbers appearing in the expansions of powers of binomials
*Binomial QMF, a perfect-reconstruction orthogonal wavelet decomposition
...
*
Multinomial
*
Simple expression
*
Compound expression
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers ( constants), variables, operations, f ...
*
Sparse polynomial In mathematics, a sparse polynomial (also lacunary polynomial or fewnomial) is a polynomial that has far fewer terms than its degree and number of variables would suggest. Examples include
*monomials, polynomials with only one term,
* binomials, po ...
References
{{algebra-stub
Elementary algebra
Polynomials