Question 368662: please help me factor this trinomial 6p^2+5p-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 6 and -6 respectively.
Now multiply the first coefficient 6 and the last coefficient -6 to get -36. Now what two numbers multiply to -36 and add to the middle coefficient 5? Let's list all of the factors of -36:
Factors of -36:
1,2,3,4,6,9,12,18
-1,-2,-3,-4,-6,-9,-12,-18 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -36
(1)*(-36)
(2)*(-18)
(3)*(-12)
(4)*(-9)
(-1)*(36)
(-2)*(18)
(-3)*(12)
(-4)*(9)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 5
| First Number | Second Number | Sum | | 1 | -36 | 1+(-36)=-35 | | 2 | -18 | 2+(-18)=-16 | | 3 | -12 | 3+(-12)=-9 | | 4 | -9 | 4+(-9)=-5 | | -1 | 36 | -1+36=35 | | -2 | 18 | -2+18=16 | | -3 | 12 | -3+12=9 | | -4 | 9 | -4+9=5 |
From this list we can see that -4 and 9 add up to 5 and multiply to -36
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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