{"title":"Factoring a Polynomial with Multiple-Roots","authors":"Feng Cheng Chang","country":null,"institution":"","volume":23,"journal":"International Journal of Computer and Information Engineering","pagesStart":3718,"pagesEnd":3722,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10086","abstract":"A given polynomial, possibly with multiple roots, is\nfactored into several lower-degree distinct-root polynomials with\nnatural-order-integer powers. All the roots, including multiplicities,\nof the original polynomial may be obtained by solving these lowerdegree\ndistinct-root polynomials, instead of the original high-degree\nmultiple-root polynomial directly.\nThe approach requires polynomial Greatest Common Divisor\n(GCD) computation. The very simple and effective process, \u201cMonic\npolynomial subtractions\" converted trickily from \u201cLonghand\npolynomial divisions\" of Euclidean algorithm is employed. It\nrequires only simple elementary arithmetic operations without any\nadvanced mathematics.\nAmazingly, the derived routine gives the expected results for the\ntest polynomials of very high degree, such as p( x) =(x+1)1000.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 23, 2008"}