SOLUTION: 3x^2+37xy-86y^2

Question 168159: 3x^2+37xy-86y^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 3 and -86 respectively.

Now multiply the first coefficient 3 and the last coefficient -86 to get -258. Now what two numbers multiply to -258 and add to the middle coefficient 37? Let's list all of the factors of -258:

Factors of -258:
1,2,3,6,43,86,129,258

-1,-2,-3,-6,-43,-86,-129,-258 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -258
(1)*(-258)
(2)*(-129)
(3)*(-86)
(6)*(-43)
(-1)*(258)
(-2)*(129)
(-3)*(86)
(-6)*(43)

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

Now which of these pairs add to 37? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 37

First Number	Second Number	Sum
1	-258	1+(-258)=-257
2	-129	2+(-129)=-127
3	-86	3+(-86)=-83
6	-43	6+(-43)=-37
-1	258	-1+258=257
-2	129	-2+129=127
-3	86	-3+86=83
-6	43	-6+43=37

From this list we can see that -6 and 43 add up to 37 and multiply to -258

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