Question 173192This question is from textbook Introductory Algebra
: Factor completely
4x^3 + 4x^2 - 80x
This question is from textbook Introductory Algebra
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 -20 respectively.
Now multiply the first coefficient 1 and the last coefficient -20 to get -20. Now what two numbers multiply to -20 and add to the middle coefficient 1? Let's list all of the factors of -20:
Factors of -20:
1,2,4,5,10,20
-1,-2,-4,-5,-10,-20 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -20
(1)*(-20)
(2)*(-10)
(4)*(-5)
(-1)*(20)
(-2)*(10)
(-4)*(5)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1
| First Number | Second Number | Sum | | 1 | -20 | 1+(-20)=-19 | | 2 | -10 | 2+(-10)=-8 | | 4 | -5 | 4+(-5)=-1 | | -1 | 20 | -1+20=19 | | -2 | 10 | -2+10=8 | | -4 | 5 | -4+5=1 |
From this list we can see that -4 and 5 add up to 1 and multiply to -20
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 factors to
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