Question 370393: How can I factor this trinomial? 4x^2 - 5xy - 6y^2
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! It'll be (ax + by)*(cx + dy)
a*b = 4
c*d = -6
ad + bc = -5
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4 has the factors 1, 2 & 4
6 has 1, 2, 3 & 6
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Since c*d = -6, the signs of c & d are different.
Since the middle term is odd, either ad or bc is odd, but not both. That means either both a & d are odd, or both c & c are odd. this eliminates some possibilities.
It requires it be (x + by)*(4x ± 3y)
a*d = ± 3
To get the -5, bc has to be either +8 or -2
-2 is not possible, so bc = ± 8, and to get -5 with ± 8 and ± 3 --> -8 and +3.
--> (x - 2y)*(4x + 3y)
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