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)
= (4r − s)(r + 3s)