Looking at we can see that the first term is and the last term is where the coefficients are 1 and -3 respectively.
Now multiply the first coefficient 1 and the last coefficient -3 to get -3. Now what two numbers multiply to -3 and add to the middle coefficient 2? Let's list all of the factors of -3:
Factors of -3:
1,3
-1,-3 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -3
(1)*(-3)
(-1)*(3)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2
First Number
Second Number
Sum
1
-3
1+(-3)=-2
-1
3
-1+3=2
From this list we can see that -1 and 3 add up to 2 and multiply to -3
Now looking at the expression , replace with (notice combines back 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 )
(