SOLUTION: Factor using AC Method. 9x^2-15x-6

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 )

-------------------------------
Answer:

So factors to
RELATED QUESTIONS
Factor each trinomial using the ac Method 15x� - 7x -2 (answered by stanbon)

Factor each Trinomial using the �ac� method. Showing work and solution. 15x� - 7x... (answered by fractalier)

Factor using ac method 4z^2 - 5z -... (answered by jim_thompson5910)

9x^2+39-14 I have to factor using ac method (answered by ankor@dixie-net.com)

5x^2-9x-2 How do you identify a factor of this trinomial using the AC... (answered by Nate)

Factor by using trial factors 9x^3-15x^2+6x (answered by Fombitz)

" How do I factor this trinomoial using the ac method?" please break it down and explain... (answered by stanbon)

2x^2+16x+2 factor using AC... (answered by Edwin McCravy)

Factor using the ac method 21x^2 + 2y -... (answered by jim_thompson5910)