#### Answer

$(x-3)(2x^2+1)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Group the terms of the given expression, $
2x^3-6x^2+x-3
,$ such that the factored form of the groupings will result to a factor that is common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression.
$\bf{\text{Solution Details:}}$
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(2x^3-6x^2)+(x-3)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
(2x^3-6x^2)+(x-3)
\\\\=
2x^2(x-3)+(x-3)
.\end{array}
Factoring the $GCF=
(x-3)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
\\\\=
(x-3)(2x^2+1)
.\end{array}