Factorise: $x^{3}-6x^{2}+11x-6$

(A) Let $f(x) = x^{3}-6x^{2}+11x-6$ be the given polynomial.
By the Factor Theorem,we test the factors of the constant term $-6$,which are $\pm 1, \pm 2, \pm 3, \pm 6$.
For $x = 1$,$f(1) = (1)^{3}-6(1)^{2}+11(1)-6 = 1-6+11-6 = 0$. Thus,$(x-1)$ is a factor.
For $x = 2$,$f(2) = (2)^{3}-6(2)^{2}+11(2)-6 = 8-24+22-6 = 0$. Thus,$(x-2)$ is a factor.
For $x = 3$,$f(3) = (3)^{3}-6(3)^{2}+11(3)-6 = 27-54+33-6 = 0$. Thus,$(x-3)$ is a factor.
Since the polynomial is of degree $3$,it can have at most $3$ linear factors.
Therefore,the factors of $x^{3}-6x^{2}+11x-6$ are $(x-1)(x-2)(x-3)$.