factor the four-term polynomial pq-3r+pr-3q?

pq - 3r + pr - 3q
(p - 3)(r + q)

Not sure how to explain it, but here goes:
I noticed that p is in terms with q and r. Therefore q and r are in a different parenthetical expression than p. Checking with 3 confirms that r and q are in one expression--3 and p must be in the other. All that's left is to look at the the negative sign and you realize the only thing it has in common with its two terms is the fact you have 3 a in each, so the 3 is negative.

pq - 3r + pr - 3q
= pq + pr - 3r - 3q
= (pq + pr) - (3r + 3q)
= p(q + r) - 3(r + q)
= p(q + r) - 3(q + r)
= (q + r)(p - 3)

p(q + r) - 3(q + r)
(q + r)(p - 3)