Question 115563: Factor using AC Method. 9x^2-15x-6
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Looking at  we can see that the first term is  and the last term is  where the coefficients are 9 and -6 respectively.
Now multiply the first coefficient 9 and the last coefficient -6 to get -54. Now what two numbers multiply to -54 and add to the middle coefficient -15? Let's list all of the factors of -54:
Factors of -54:
1,2,3,6,9,18,27,54
-1,-2,-3,-6,-9,-18,-27,-54 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -54
(1)*(-54)
(2)*(-27)
(3)*(-18)
(6)*(-9)
(-1)*(54)
(-2)*(27)
(-3)*(18)
(-6)*(9)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to -15? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -15
| First Number | Second Number | Sum | | 1 | -54 | 1+(-54)=-53 | | 2 | -27 | 2+(-27)=-25 | | 3 | -18 | 3+(-18)=-15 | | 6 | -9 | 6+(-9)=-3 | | -1 | 54 | -1+54=53 | | -2 | 27 | -2+27=25 | | -3 | 18 | -3+18=15 | | -6 | 9 | -6+9=3 |
From this list we can see that 3 and -18 add up to -15 and multiply to -54
Now looking at the expression , replace  with  (notice adds up to . So it is equivalent to )
Now let's factor  by grouping:
 Group like terms
 Factor out the GCF of  out of the first group. Factor out the GCF of out of the second group
 Since we have a common term of  , we can combine like terms
So factors to
So this also means that factors to (since is equivalent to )
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Answer:
So factors to
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