$12 x^{2}-7 x+1$

Here co-efficient of $\quad x^{2}=12$

Co-efficient of $x=-7$

and constant term $=1$                             $\therefore $ $a =12, \,b =-\,7, \,c =1$

Now,            $l+ m =-7$ and $lm = ac =12 \times 1$

$\therefore$ we have $l=(-4)$ and $m =(-3)$ i.e. $b =-7=(-4-3)$

Now, $12 x^{2}-7 x+1=12 x^{2}-4 x-3 x+1$

                $=4 x(3 x-1)-1(3 x-1)=(3 x-1)(4 x-1)$

Thus,   $12 x^{2}-7 x+1=(3 x-1)(4 x-1)$