Question 119713: Was I able to factor this correctly?
4x^2-15x-25
=(2x+5)(2x+5)
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 4 and -25 respectively.
Now multiply the first coefficient 4 and the last coefficient -25 to get -100. Now what two numbers multiply to -100 and add to the middle coefficient -15? Let's list all of the factors of -100:
Factors of -100:
1,2,4,5,10,20,25,50
-1,-2,-4,-5,-10,-20,-25,-50 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -100
(1)*(-100)
(2)*(-50)
(4)*(-25)
(5)*(-20)
(-1)*(100)
(-2)*(50)
(-4)*(25)
(-5)*(20)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to -15? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -15
| First Number | Second Number | Sum | | 1 | -100 | 1+(-100)=-99 | | 2 | -50 | 2+(-50)=-48 | | 4 | -25 | 4+(-25)=-21 | | 5 | -20 | 5+(-20)=-15 | | -1 | 100 | -1+100=99 | | -2 | 50 | -2+50=48 | | -4 | 25 | -4+25=21 | | -5 | 20 | -5+20=15 |
From this list we can see that 5 and -20 add up to -15 and multiply to -100
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 )
So factors to
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