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Looking at we can see that the first term is and the last term is where the coefficients are 1 and -16 respectively.
Now multiply the first coefficient 1 and the last coefficient -16 to get -16. Now what two numbers multiply to -16 and add to the middle coefficient 6? Let's list all of the factors of -16:
Factors of -16:
1,2,4,8
-1,-2,-4,-8 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -16
(1)*(-16)
(2)*(-8)
(-1)*(16)
(-2)*(8)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 6
First Number
Second Number
Sum
1
-16
1+(-16)=-15
2
-8
2+(-8)=-6
-1
16
-1+16=15
-2
8
-2+8=6
From this list we can see that -2 and 8 add up to 6 and multiply to -16
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 )
(