Answer
$(x+2)(3x+5)$.
Work Step by Step
The given expression is
$=3(x+1)^{2}-5(x+1)+2$
Substitute $x+1=u$.
$=3(u)^2-5u+2$
Simplify.
$=3u^2-5u+2$
Rewrite $5u$ as $3u+2u$.
$=3u^2+3u+2u+2$
Factor.
$=3u(u+1)+2(u+1)$
$=(u+1)(3u+2)$.
Substitute back $u=x+1$.
$=((x+1)+1)(3(x+1)+2)$.
Simplify.
$=(x+1+1)(3x+3+2)$.
$=(x+2)(3x+5)$.
