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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