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Looking at we can see that the first term is and the last term is where the coefficients are 2 and -3 respectively.
Now multiply the first coefficient 2 and the last coefficient -3 to get -6. Now what two numbers multiply to -6 and add to the middle coefficient -8? Let's list all of the factors of -6:
Factors of -6:
1,2,3,6
-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -6
(1)*(-6)
(2)*(-3)
(-1)*(6)
(-2)*(3)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to -8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -8
First Number
Second Number
Sum
1
-6
1+(-6)=-5
2
-3
2+(-3)=-1
-1
6
-1+6=5
-2
3
-2+3=1
None of these pairs of factors add to -8. So the expression cannot be factored
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