SOLUTION: if x-1 and x+1 are both factors of the equation x^3+px^2+qx+6=0

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Question 960471: if x-1 and x+1 are both factors of the equation x^3+px^2+qx+6=0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the other factor +x+-+a+
+%28+x+-+1+%29%2A%28+x+%2B+1+%29%2A%28+x+-+a+%29+=+%28+x%5E2+-1+%29%2A%28+x+-+a+%29+
+x%5E3+-+a%2Ax%5E2+-+x+%2B+a+
The given equation is:
+x%5E3+%2B+p%2Ax%5E2+%2B+q%2Ax+%2B+6+=+0+
+a+=+-p+
+q+=+-1+
+a+=+6+
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The other factor is +x+-%28-p%29+,
or +x+%2B+p+
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the equation is:
+x%5E3+-+6x%5E2+-+x+%2B+6+=+0+
check:
+%28+x+-+1+%29%2A%28+x+%2B+1+%29%2A%28+x+-+6+%29+
+%28+x%5E2+-+1+%29%2A%28+x+-+6+%29+
+x%5E3+-+6x%5E2+-+x+%2B+6+
OK