Question 190281: Factor
4x^2+16x-48
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
 Start with the given expression
 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 1 and -12 respectively.
Now multiply the first coefficient 1 and the last coefficient -12 to get -12. Now what two numbers multiply to -12 and add to the middle coefficient 4? Let's list all of the factors of -12:
Factors of -12:
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -12
(1)*(-12)
(2)*(-6)
(3)*(-4)
(-1)*(12)
(-2)*(6)
(-3)*(4)
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 | -12 | 1+(-12)=-11 | | 2 | -6 | 2+(-6)=-4 | | 3 | -4 | 3+(-4)=-1 | | -1 | 12 | -1+12=11 | | -2 | 6 | -2+6=4 | | -3 | 4 | -3+4=1 |
From this list we can see that -2 and 6 add up to 4 and multiply to -12
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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