Question 112000: Please help me, I am learning how to factor and a few are stumping me.
(6A^2 - 5A-2)
Thanks
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 -2 respectively.
Now multiply the first coefficient 6 and the last coefficient -2 to get -12. Now what two numbers multiply to -12 and add to -5? Let's list all of the factors of -12:
Factors of -12:
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -12
(1)*(-12)
(2)*(-6)
(3)*(-4)
(-1)*(12)
(-2)*(6)
(-3)*(4)
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 | -12 | 1+(-12)=-11 | | 2 | -6 | 2+(-6)=-4 | | 3 | -4 | 3+(-4)=-1 | | -1 | 12 | -1+12=11 | | -2 | 6 | -2+6=4 | | -3 | 4 | -3+4=1 |
None of these pairs of factors add to -5. So the expression cannot be factored
Make sure you copied the problem down correctly
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