SOLUTION: I am a new student and the SOLs are very close and I'm very lost! Now were working on factoring numbers the problems 3x^2-9x+6

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Question 738900: I am a new student and the SOLs are very close and I'm very lost! Now were working on factoring numbers the problems 3x^2-9x+6
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
factor:
+3x%5E2+-+9x+%2B+6+
Set it equal to zero
+3x%5E2+-+9x+%2B+6++=+0+
Divide both sides by +3+
+x%5E2+-+3x+%2B+2+=+0+
Note that +%28-2%29%2A%28-1%29+=+2+
and +%28-2%29+%2B+%28-1%29+=+-3+
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This leads me to the solution
+%28+x+-+2+%29%2A%28+x+-+1+%29+=+0+
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There is the more drawn-out way, also
You know the solution will look like
+%28+x+%2B+r%5B1%5D+%29%2A%28+x+%2B+r%5B2%5D+%29+=+0+
where both of+r%5B1%5D+ and +r%5B2%5D+
can be positive or negative.
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Expanding:
+x%5E2+%2B+r%5B1%5D%2Ax+%2B+r%5B2%5D%2Ax+%2B+r%5B1%5D%2Ar%5B2%5D+=+0+
+x%5E2+%2B+%28+r%5B1%5D+%2B+r%5B2%5D+%29%2Ax+%2B+r%5B1%5D%2Ar%5B2%5D+=+0+
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You are given:
+x%5E2+-+3x+%2B+2+=+0+
+r%5B1%5D+%2B+r%5B2%5D+=+-3+
+r%5B1%5D%2Ar%5B2%5D+=+2+
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This shows how I got my solution