Using grouping method, we have:

So we are looking for 2 terms whose product is −12r2s2and whose sum is 11rs.

Those 2 terms will be 12rs and −rs.

So we can factor our trinomial as follows:

4r2 + 11rs − 3s2

= 4r2 + 12rs rs − 3s2

= (4r2 + 12rs) − (rs + 3s2)

= 4r(r + 3s) − s(r + 3s)

= (4rs)(r + 3s)