Write the coefficient of $x^{2}$ in each of the following:
$(i)$ $(x-1)(3 x-4)$
$(ii)$ $(2 x-5)(2 x^{2}-3 x+1)$

(N/A) $(i)$ The given polynomial can be expanded as:
$(x-1)(3 x-4) = 3 x^{2} - 4 x - 3 x + 4$
$= 3 x^{2} - 7 x + 4$
Comparing this with the standard form $ax^{2} + bx + c$,the coefficient of $x^{2}$ is $3$.
$(ii)$ The given polynomial can be expanded as:
$(2 x-5)(2 x^{2}-3 x+1) = 2 x(2 x^{2}-3 x+1) - 5(2 x^{2}-3 x+1)$
$= 4 x^{3} - 6 x^{2} + 2 x - 10 x^{2} + 15 x - 5$
$= 4 x^{3} - 16 x^{2} + 17 x - 5$
Comparing this with the standard form,the coefficient of $x^{2}$ is $-16$.