Answer
$(a+2b)(3a-7b)$
Work Step by Step
$3a^{2}-ab-14b^{2}$
... Searching for two factors of $ac=-42$ whose sum is $b=-1,$
we find$\qquad 6$ and $-7.$
Rewrite the middle term and factor in pairs:
$=3a^{2}+6ab-7ab-14b^{2}=$
$=3a(a+2b)-7b(a+2b)$
= $(a+2b)(3a-7b)$