SOLUTION: Factor: x^2+6x-16

Question 125884: Factor:

x^2+6x-16

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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 )

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Answer:
So factors to

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