Answer
$(3x+2)(3x+1)$
Work Step by Step
$(3x-1)^{2}+5(3x-1)+6$
By substituting $ 3x-1 = t$, we get,
$t^{2}+5t+6$
In this trinomial $t^{2}+5t+6$, $a=1$, $b=5$ and $c=6$.
Splitting the middle term $b$ into two numbers whose product is $6$ $(a \times c)$ and whose sum is $(b)$ $5$. The numbers are $3$ and $2$.
$=t^{2}+3t+2t+6$
Factor out by grouping.
$=(t^{2}+3t)+(2t+6)$
$=(t(t+3)+2(t+3))$
$=(t+3)(t+2)$
Substituting $ t$ value,
$=(3x-1+3)(3x-1+2)$
$=(3x+2)(3x+1)$
