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 4? 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 two negative numbers multiplied together make a positive number
Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4
First Number
Second Number
Sum
1
6
1+6=7
2
3
2+3=5
-1
-6
-1+(-6)=-7
-2
-3
-2+(-3)=-5
None of these pairs of factors add to 4. So the expression cannot be factored
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