SOLUTION: Factor: 12𝑥^3+𝑥^2−20𝑥

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Question 1117946: Factor:
12𝑥^3+𝑥^2−20𝑥
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
12x^3 + x^2 - 20x
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= x*(12x^2 + x - 20)
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12x^2 + x - 20 = (ax + b)*(cx + d)
a & c are positive.
d & d have different signs.
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For ac & bd, one is even, one is odd.
Try different combinations of factors of 12 & 20.
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Factoring is often trial & error.
You get better at it with practice.
Having someone do it for you doesn't help you.
==================
Close call.
You were close to learning something.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
12x%5E3%2Bx%5E2-20x

x%2812x%5E2%2Bx-20%29

Look at all the combinations for the quadratic factor that you can make and see which one works. 

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(12x  1)(x  20)
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(12x 2)(x  10)
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(12x  20)(x  1)
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(12x  10)(x  2)
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(12x 4)(x  5)
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(12  5)(x  4)
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..
.
still many more combinations to look at...

If you try general solution formula for a quadratic expression (to find roots), then you would start with
x=%28-1%2B-+sqrt%281%2B4%2A12%2A20%29%29%2F24
Showing roots to be system%28-4%2F3%2Cand%2C5%2F4%29.

With some integer factor k, your quadratic factor would be
k%28x%2B4%2F3%29%28x-5%2F4%29
which you should be able to work with and finish.