
factoring allone polynomials using the grouping method

(Example)


The method of grouping terms can be used to factor allone polynomials, i.e. polynomials of the form
when is composite. (When is prime, these polynomials are irreducible, so there is nothing to do in that case.)
Let us consider a few examples:
:
:
:
Combining this result with the factorization we have for the case , we obtain the following:
:
:
It might be worth pointing out that the polynomials produced by this factorization are not all irreducible. For instance,
However, to obtain this factorization, one needs to use some techique other than the grouping method. Likewise. the polynomial is also reducible.

"factoring allone polynomials using the grouping method" is owned by rspuzio.


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See Also: all one polynomial, cyclotomic polynomial
This object's parent.
Crossreferences: reducible, irreducible, prime, composite, polynomials, allone polynomials, factor, terms
This is version 10 of factoring allone polynomials using the grouping method, born on 20050306, modified 20050809.
Object id is 6851, canonical name is FactoringAllOnePolynomialsUsingTheGroupingMethod.
Accessed 1765 times total.
Classification:
AMS MSC:  13P05 (Commutative rings and algebras :: Computational aspects of commutative algebra :: Polynomials, factorization) 



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