SOLUTION: Factor the polynomial completely 12b^3-86b^2+14b Thanks for your help!

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Question 105099: Factor the polynomial completely
12b^3-86b^2+14b
Thanks for your help!
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
12b%5E3-86b%5E2%2B14b=2b%286b%5E2-43b%2B7%29
To factor 6b%5E2-43b%2B7, first, read my lesson entitled,"Factoring trinomials: SHORTCUT!!!" then go back to this page.
By the quadratic formula,
b=%2843%2B-sqrt%2843%5E2-4%2A6%2A7%29%29%2F%282%2A6%29
b=%2843%2B-sqrt%281849-168%29%29%2F%2812%29
b=%2843%2Bsqrt%281681%29%29%2F%2812%29 or b=%2843-sqrt%281681%29%29%2F%2812%29
b=%2843%2B41%29%2F%2812%29 or b=%2843-41%29%2F%2812%29
b=84%2F12 or b=2%2F12
b=7 or b=1%2F6
If b=7,
b-7=0
If b=1%2F6,
6b-1=0
Thus,
6b%5E2-43b%2B7=%28b-7%29%286b-1%29
And therefore,
12b%5E3-86b%5E2%2B14b=2b%28b-7%29%286b-1%29

Power up,
HyperBrain!