What is the complete factorization of the polynomial x3 - 3x2 plus x - 3?

To factor the polynomial ( x^3 - 3x^2 + x - 3 ), we first apply the Rational Root Theorem and test possible rational roots. After testing, we find that ( x = 3 ) is a root. Using synthetic division, we divide the polynomial by ( (x - 3) ) to obtain ( x^2 + 1 ). Thus, the complete factorization is ( (x - 3)(x^2 + 1) ).