Feng Cheng Chang
Factoring a Polynomial with MultipleRoots
3718 - 3721
2008
2
11
International Journal of Computer and Information Engineering
https://publications.waset.org/pdf/10086
https://publications.waset.org/vol/23
World Academy of Science, Engineering and Technology
A given polynomial, possibly with multiple roots, is
factored into several lowerdegree distinctroot polynomials with
naturalorderinteger powers. All the roots, including multiplicities,
of the original polynomial may be obtained by solving these lowerdegree
distinctroot polynomials, instead of the original highdegree
multipleroot polynomial directly.
The approach requires polynomial Greatest Common Divisor
(GCD) computation. The very simple and effective process, “Monic
polynomial subtractions" converted trickily from “Longhand
polynomial divisions" of Euclidean algorithm is employed. It
requires only simple elementary arithmetic operations without any
advanced mathematics.
Amazingly, the derived routine gives the expected results for the
test polynomials of very high degree, such as p( x) (x1)1000.
Open Science Index 23, 2008