Trinomial
Polynomial that has three terms
In elementary algebra, a trinomial is a polynomial consisting of three terms or monomials.[1]
Examples of trinomial expressions
- with variables
- with variables
- with variables
- , the quadratic polynomial in standard form with variables.[note 1]
- 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.[2]
Some notable trinomials
- The quadratic trinomial in standard form (as from above):
- 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.
See also
- Trinomial expansion
- Monomial
- Binomial
- Multinomial
- Simple expression
- Compound expression
- Sparse polynomial
Notes
- ^ Quadratic expressions are not always trinomials, the expressions' appearance can vary.
References
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- Univariate
- Bivariate
- Multivariate
- Monomial
- Binomial
- Trinomial
- Irreducible
- Square-free
- Homogeneous
- Quasi-homogeneous
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