Looking at we can see that the first term is and the last term is where the coefficients are 1 and -4 respectively.
Now multiply the first coefficient 1 and the last coefficient -4 to get -4. Now what two numbers multiply to -4 and add to the middle coefficient 3? Let's list all of the factors of -4:
Factors of -4:
1,2
-1,-2 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -4
(1)*(-4)
(-1)*(4)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 3
First Number
Second Number
Sum
1
-4
1+(-4)=-3
-1
4
-1+4=3
From this list we can see that -1 and 4 add up to 3 and multiply to -4
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 )
(