The factors of polynomial $x^3-6x^2+11x-6$ are

Let $f(x)=x^3-6x^2+11x-6$.Test $x=1$ using the Factor Theorem:
$$f(1)=1^3-6(1{)}^2+11(1)-6=1-6+11-6=0$$
Since $f(1)=0$, $(x-1)$ is a factor.Divide $f(x)$ by $(x-1)$ using polynomial long division or synthetic division to find the remaining quadratic factor:
$$x^3-6x^2+11x-6=(x-1)(x^2-5x+6)$$
Factor the quadratic expression $x^2-5x+6$:
$$x^2-5x+6=x^2-2x-3x+6=x(x-2)-3(x-2)=(x-2)(x-3)$$
Thus, the complete factors are $(x-1)(x-2)(x-3)$.