Factorise:

We have:

$x^{3}-3 x^{2}+x-3=\left(x^{3}-3 x^{2}\right)+(x-3)$

$=x^{2}(x-3)+1(x-3)$

$=(x-3)\left(x^{2}+1\right)$

$\therefore x^{3}-3 x^{2}+x-3=(x-3)\left(x^{2}+1\right)$