This article is about mathematics. For the use in taxonomy, see
Trinomial name. For the use identifying archaeological sites in the United States, see
Smithsonian trinomial.
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.
^Corless, R. M.; Gonnet, G. H.; Hare, D. E. G.; Jerey, D. J.; Knuth, D. E. (1996).
"On the Lambert W Function"(PDF). Advances in Computational Mathematics. 5 (1): 329–359.
doi:
10.1007/BF02124750.
This article is about mathematics. For the use in taxonomy, see
Trinomial name. For the use identifying archaeological sites in the United States, see
Smithsonian trinomial.
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.
^Corless, R. M.; Gonnet, G. H.; Hare, D. E. G.; Jerey, D. J.; Knuth, D. E. (1996).
"On the Lambert W Function"(PDF). Advances in Computational Mathematics. 5 (1): 329–359.
doi:
10.1007/BF02124750.