Hi,

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

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







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

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

 

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
 18s^3+87s^2-126s



3s(6s^2+29s-42)

-------------

Now you factor 6s^2+29s-42

---------------

Check pairs of factors for 6 & for 42.

6 = 1*6 or 2*3

For 42,

1*42

2*21

3*14

6*7

-----

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 +

---

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.

---

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

==================

Do you know how to find the discriminant?  That's the only way to shorten the process.





 

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