We usually use the factorization method to factor second-degree or quadratic polynomials. For higher degrees, we can use the below-given procedure to factor the polynomial:Step 1: Use the synthetic division of
For holomorphic functions Cauchy's index is based on contour integration, but in the special case of polynomials it can effectively be calculated via Sturm chains using euclidean division as in the real case. In this way we provide an algebraic proof of Cauchy's theorem for polynomials over ...
Let R = prem(G; ASC), then from the computation procedure of the pseudo division pro- cedure, we have the following important remainder formula: (2.1) JG ≡ R [A 1 ,··· , A p ] where J is a product of powers of the initials and separants of the polynomials in ASC ...
Now let us use synthetic division to determine the other factors of the function aside from ( x-3 ). The diagram below shows the results of dividing V (x) = 2x3– 7x2+ 2x+3 by the factor ( x-3 ). The value x= 3 comes from the divisor ( x-3 ). The coefficients of the di...