SOLUTION: I need help factoring this completely. 6x^2+5xy-y^2

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Question 886110: I need help factoring this completely.
6x^2+5xy-y^2
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+6x%5E2+%2B+5x%2Ay+-+y%5E2+
I can say it must be of the form:
+%28+a%2Ax+%2B+y+%29%2A%28+c%2Ax+-+y+%29+
Now I can expand this
+a%2Ac%2Ax%5E2+%2B+c%2Ax%2Ay+-+a%2Ax%2Ay+-+y%5E2+
+a%2Ac%2Ax%5E2+%2B+%28+c-a+%29%2Ax%2Ay+-+y%5E2+
--------------------------------
Comparing this to the problem, I can say:
(1) +a%2Ac+=+6+
(2) +c+-+a+=+5+
-----------------
(1) +c+=+6%2Fa+
and
(2) +6%2Fa+-+a+=+5+
(2) +6+-+a%5E2+=+5a+
(2) +a%5E2+%2B+5a+-+6+=+0+
By inspection, I see:
(2) +%28+a+%2B+6+%29%2A%28+a+-+1+%29+=+0+
(2) +a+=+-6+ ( You can use this value to find a different +c+ )
(2) +a+=+1+
and
(2) +c+-+a+=+5+
(2) +c+-+1+=+5+
(2) +c+=+6+
-------------
The factors are:
+%28+a%2Ax+%2B+y+%29%2A%28+c%2Ax+-+y+%29+
+%28+x+%2B+y+%29%2A%28+6x+-+y+%29+
Hope this helps