SOLUTION: Factor: 8x^2-16-28x

Question 200296: Factor: 8x^2-16-28x
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression.

Rearrange the terms.

Factor out the GCF

Now let's focus on the inner expression

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Looking at we can see that the first term is and the last term is where the coefficients are 2 and -4 respectively.

Now multiply the first coefficient 2 and the last coefficient -4 to get -8. Now what two numbers multiply to -8 and add to the middle coefficient -7? Let's list all of the factors of -8:

Factors of -8:
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 -8
(1)*(-8)
(2)*(-4)
(-1)*(8)
(-2)*(4)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to -7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -7

First Number	Second Number	Sum
1	-8	1+(-8)=-7
2	-4	2+(-4)=-2
-1	8	-1+8=7
-2	4	-2+4=2

From this list we can see that 1 and -8 add up to -7 and multiply to -8

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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So our expression goes from and factors further to

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Answer:

So completely factors to

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