SOLUTION: x^2-11xy-42y^2

Question 116200: x^2-11xy-42y^2
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 -42 respectively.

Now multiply the first coefficient 1 and the last coefficient -42 to get -42. Now what two numbers multiply to -42 and add to the middle coefficient -11? Let's list all of the factors of -42:

Factors of -42:
1,2,3,6,7,14,21,42

-1,-2,-3,-6,-7,-14,-21,-42 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -42
(1)*(-42)
(2)*(-21)
(3)*(-14)
(6)*(-7)
(-1)*(42)
(-2)*(21)
(-3)*(14)
(-6)*(7)

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

Now which of these pairs add to -11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -11

First Number	Second Number	Sum
1	-42	1+(-42)=-41
2	-21	2+(-21)=-19
3	-14	3+(-14)=-11
6	-7	6+(-7)=-1
-1	42	-1+42=41
-2	21	-2+21=19
-3	14	-3+14=11
-6	7	-6+7=1

From this list we can see that 3 and -14 add up to -11 and multiply to -42

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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Answer:

So factors to
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