SOLUTION: Factor Completely 6x^3 - 16x^2 - 6x

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Question 474274: Factor Completely
6x^3 - 16x^2 - 6x
Found 2 solutions by MathLover1, josmiceli:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

6x%5E3+-+16x%5E2+-+6x
x%286x%5E2+-+16x+-+6%29.........6x%5E2+-+16x+-+6 cannot be factored, so you
can only have x%286x%5E2+-+16x+-+6%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+6x%5E3+-+16x%5E2+-+6x+
+2x%2A%283x%5E2+-+8x+-+3%29+
Find the factors of the quadratic
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+3+
+b+=+-8+
+c+=+-3+
x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%2A3%2A%28-3%29+%29%29%2F%282%2A3%29+
x+=+%28+8+%2B-+sqrt%28+64+%2B+36+%29%29+%2F+6+
x+=+%28+8+%2B-+sqrt%28+100+%29%29+%2F+6+
x+=+%28+8+%2B+10%29+%2F+6+
+x+=+18%2F6+
(1) +x+=+3+
and
x+=+%28+8+-+10%29+%2F+6+
+x+=+-2%2F6+
(2) +x+=+-1%2F3+
Now rewrite (1) and (2) as:
(1) +x+-+3+=+0+
(2) +x+%2B+1%2F3+=+0+
(2) +3x+%2B+1+=+0+
so,
+3x%5E2+-+8x+-+3++=+%28+x+-+3+%29%2A%28+3x+%2B+1+%29+
The complete factorization is:
+2x%2A%28+x+-+3+%29%2A%28+3x+%2B+1+%29+
-----------
check:
+2x%2A%283x%5E2+-+9x+%2B+x+-+3%29+
+2x%2A%283x%5E2+-+8x+-+3%29+
+6x%5E3+-+16x%5E2+-+6x+
OK