Answer
$2x(x+1)(5x+7)$
Work Step by Step
$ 10x^{3}+24x^{2}+14x\qquad$...factor out the common term, $2x$.
$=2x(5x^{2}+12x+7)$
Two factors of $ac=+35$, whose sum is $b=+12$
are $5$ and $7$.
Rewrite $12x$ as $5x+7x$ and factor in pairs.
$2x(5x^{2}+12x+7)$
$=2x(5x^{2}+5x+7x+7)$
$=2x[5x(x+1)+7(x+1)]$
=$2x(x+1)(5x+7)$
