Using grouping method, we have:
So we are looking for 2 terms whose product is −42x2y2 and whose sum is xy.
A little bit of thinking gives us: 7xy and −6xy.
So we can factor our trinomial as follows:
3x2 + xy − 14y2
= 3x2 + 7xy − 6xy − 14y2
= (3x2 + 7xy) − (6xy + 14y2)
= x(3x + 7y) − 2y(3x + 7y)
= (x − 2y)(3x + 7y)
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