Chapter 6 - Section 6.2 - Factoring Trinomials Whose Leading Coefficient is 1 - Exercise Set - Page 436: 51

$2r(r+1)(r+2)$

Factoring the $GCF= 2r ,$ the given expression, $ 2r^3+6r^2+4r ,$ is equivalent to \begin{array}{l}\require{cancel} 2r(r^2+3r+2) .\end{array} The trinomial expression above has $c= 2 $ and $b= 3 .$ The possible factors of $c$ are $ \{ 1,2 \} ,\{ -1,-2 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ 1,2 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} 2r(r+1)(r+2) .\end{array}