SOLUTION: {{{x^2 - 6xy - 40y^2}}} Factor completely. I do not understand how to do this. Its frustrating because I think I understand but I am still getting the answer wrong. Please h

Question 251213:
Factor completely.
I do not understand how to do this. Its frustrating because I think I understand but I am still getting the answer wrong. Please help!
Found 2 solutions by scott8148, jim_thompson5910:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
you are looking for factors of -40 that "combine" to give -6

like -10 and 4 ___ -10 + 4 = -6

(x - 10y) (x + 4y)
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 1 and -40 respectively.

Now multiply the first coefficient 1 and the last coefficient -40 to get -40. Now what two numbers multiply to -40 and add to the middle coefficient -6? Let's list all of the factors of -40:

Factors of -40:
1,2,4,5,8,10,20,40

-1,-2,-4,-5,-8,-10,-20,-40 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -40
(1)*(-40)
(2)*(-20)
(4)*(-10)
(5)*(-8)
(-1)*(40)
(-2)*(20)
(-4)*(10)
(-5)*(8)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to -6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -6

First Number Second Number Sum
1 -40 1+(-40)=-39
2 -20 2+(-20)=-18
4 -10 4+(-10)=-6
5 -8 5+(-8)=-3
-1 40 -1+40=39
-2 20 -2+20=18
-4 10 -4+10=6
-5 8 -5+8=3

From this list we can see that 4 and -10 add up to -6 and multiply to -40

Now looking at the expression , replace with (notice combines back 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 )

------------------------------------------------------------

Answer:
So factors to

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First Number	Second Number	Sum
1	-40	1+(-40)=-39
2	-20	2+(-20)=-18
4	-10	4+(-10)=-6
5	-8	5+(-8)=-3
-1	40	-1+40=39
-2	20	-2+20=18
-4	10	-4+10=6
-5	8	-5+8=3