SOLUTION: 18s^3+87s^2-126s 3s(6s^2+29s-42) what now?

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Question 820895: 18s^3+87s^2-126s
3s(6s^2+29s-42)
what now?
Found 2 solutions by ewatrrr, Alan3354:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

18s^3+87s^2-126s

3s(6s^2+29s-42)   |Good Work

s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

s+=+%28-29+%2B-+sqrt%28+1849+%29%29%2F%2812%29+

s+=+%28-29+%2B-+43%29%2F%2812%29+

       s =14/12 = 7/6.   s = -72/12 = -6

3s(s - 7/6)(s+ 6)

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
18s^3+87s^2-126s
3s(6s^2+29s-42)
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Now you factor 6s^2+29s-42
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Check pairs of factors for 6 & for 42.
6 = 1*6 or 2*3
For 42,
1*42
2*21
3*14
6*7
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It'll be (ms + p)*(ns + q)
m*n = 6 and p*q = -42
Obviously, the signs of p & q are different.
m & n are both +
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It's trial and error, but another clue is that 29 is an odd number, so only one of the products mq & ps is odd. That is, one is even, one is odd.
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Try 1 & 6 for m & n
(s - 1)*(6s + 42) NG, and notice both products are even --> 3 & 14 is NG too
(s - 2)*(6s + 21) --> -9s NG
(s - 6)*(6s + 7) --> -29s NG but only the sign of 29 is wrong.
Swap signs
(s + 6)*(6s - 7) = 6s^2 + 29s - 42
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Do you know how to find the discriminant? That's the only way to shorten the process.