SOLUTION: Was I able to factor this correctly? 4x^2-15x-25 =(2x+5)(2x+5)

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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