factor theorem
If is a polynomial over a ring with identity, then is a factor if and only if is a root (that is, ).
This theorem is of great help for finding factorizations of higher degree polynomials. As example, let us think that we need to factor the polynomial . With some help of the rational root theorem we can find that is a root (that is, ), so we know must be a factor of the polynomial. We can write then
where the polynomial can be found using long or synthetic division of between . In our case which can be easily factored as . We conclude that
Title | factor theorem |
Canonical name | FactorTheorem |
Date of creation | 2013-03-22 12:17:24 |
Last modified on | 2013-03-22 12:17:24 |
Owner | drini (3) |
Last modified by | drini (3) |
Numerical id | 10 |
Author | drini (3) |
Entry type | Theorem |
Classification | msc 12D10 |
Classification | msc 12D05 |
Synonym | root theorem |
Related topic | Polynomial |
Related topic | RationalRootTheorem |
Related topic | Root |
Related topic | APolynomialOfDegreeNOverAFieldHasAtMostNRoots |