Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$(x-3)(2x^2+1)$
$\bf{\text{Solution Outline:}}$ 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}