Question 171356: Factoring Polynomials
20q^2+28q-24
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 5 and -6 respectively.
Now multiply the first coefficient 5 and the last coefficient -6 to get -30. Now what two numbers multiply to -30 and add to the middle coefficient 7? Let's list all of the factors of -30:
Factors of -30:
1,2,3,5,6,10,15,30
-1,-2,-3,-5,-6,-10,-15,-30 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -30
(1)*(-30)
(2)*(-15)
(3)*(-10)
(5)*(-6)
(-1)*(30)
(-2)*(15)
(-3)*(10)
(-5)*(6)
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 | -30 | 1+(-30)=-29 | | 2 | -15 | 2+(-15)=-13 | | 3 | -10 | 3+(-10)=-7 | | 5 | -6 | 5+(-6)=-1 | | -1 | 30 | -1+30=29 | | -2 | 15 | -2+15=13 | | -3 | 10 | -3+10=7 | | -5 | 6 | -5+6=1 |
From this list we can see that -3 and 10 add up to 7 and multiply to -30
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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