International Journal of Mechatronics, Electrical and Computer Technology Vol. 4(13), Oct, 2014, pp. 1650-1656, ISSN: 2305-0543 Available online at: http://www.aeuso.org © Austrian E-Journals of Universal Scientific Organization - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1650 Dixon Resultant without Extraneous Factors Seyedmehdi Karimisangdehi * , Shahrbanoo Akbarpoor, Azadeh Valipour, Babak Khabiri and Seyedrabie Moosaviankhatir Faculty member of Islamic Azad University, Jouybar Branch, IRAN *Corresponding Author's E-mail: 3yedmehD@gmail.com Abstract Extraneous factors are unwanted parameters which appear in the process of eliminating variables in a symbolic polynomial system. This paper is intended to present the conditions, under which the Dixon resultant formulation is exact which implied as there is not any extraneous factors in determinante of Dixon matrix. Like other matrix based methods, the Dixon method is not exempt from the existence of extraneous factors along with the resultant which together is called projection operator; however, recognition of these factors takes a long process, and sometimes the presence of them can make computing the projection operator impractical. As a matter of fact, under such conditions, the projection operators are exactly, up to a constant factor, resultant. Keywords: Elimination Theory, Resultant, Dixon Construction, Extraneous Factors. 1. Introduction Resultant theory has a long mathematical story, starting with the resolution of linear polynomials system. The first explicit construction so called resultant of two univariate polynomials, proposed by L. Euler in 1764 [1] and E. B´ezout 1779 [2], was followed by the well known Dialytic method of Sylvester in 1858 [3]. The generalizations of this method to multivariate polynomials appeared after 1860 at which point intensive studies were initiated by Salmon [4], Macaulay [5], Dixon in 1908 [6] and Van Der Waerden in 1950 [7], in this area. But after this point it started to be forgotten, and until 1990’s, it did