Answer: The correct option is
(A) \((p-3)(q+r).\)
Step-by-step explanation: We are given to factor the following term polynomial :
\(P=pq-3r+pr-3q~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We will be using the following factorization formula :
\(ab+ac+db+dc=(a+d)(b+c).\)
From (i), we get
\(P\\\\=pq-3r+pr-3q\\\\=q(p-3)+r(p-3)\\\\=(p-3)(q+r).\)
Thus, the required factored form is \((p-3)(q+r).\)
Option (A) is CORRECT.