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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 1? 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 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1
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
From this list we can see that -2 and 3 add up to 1 and multiply to -6
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 )
(