Answer
$(x-3)(x+1)(x-1)$
Work Step by Step
Group the first two terms together and group the last two terms together.
$x^3-3x^2-x+3=(x^3-3x^2)+(-x+3)$
Factor out the GCF in each group.
$=x^2(x-3)+(-1)(x-3)$
$=x^2(x-3)-1(x-3)$
Factor out $(x-3)$.
$=(x-3)(x^2-1)$
$=(x-3)(x^2-1^2)$
Use special formula $a^2-b^2=(a+b)(a-b)$ where $a=x$ and $b=1$.
$=(x-3)(x+1)(x-1)$
Hence, the completely factored form of the given expression is $(x-3)(x+1)(x-1)$.
