Looking at we can see that the first term is and the last term is where the coefficients are 1 and -21 respectively.
Now multiply the first coefficient 1 and the last coefficient -21 to get -21. Now what two numbers multiply to -21 and add to the middle coefficient 4? Let's list all of the factors of -21:
Factors of -21:
1,3,7,21
-1,-3,-7,-21 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -21
(1)*(-21)
(3)*(-7)
(-1)*(21)
(-3)*(7)
note: remember, the product of a negative and a positive number is a negative 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
-21
1+(-21)=-20
3
-7
3+(-7)=-4
-1
21
-1+21=20
-3
7
-3+7=4
From this list we can see that -3 and 7 add up to 4 and multiply to -21
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 )
(