SOLUTION: Factor completely. 6x^2�xy�5y^2

Question 117828: Factor completely. 6x^2�xy�5y^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 6 and -5 respectively.

Now multiply the first coefficient 6 and the last coefficient -5 to get -30. Now what two numbers multiply to -30 and add to the middle coefficient -1? Let's list all of the factors of -30:

Factors of -30:
1,2,3,5,6,10,15,30

-1,-2,-3,-5,-6,-10,-15,-30 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -30
(1)*(-30)
(2)*(-15)
(3)*(-10)
(5)*(-6)
(-1)*(30)
(-2)*(15)
(-3)*(10)
(-5)*(6)

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

Now which of these pairs add to -1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -1

First Number	Second Number	Sum
1	-30	1+(-30)=-29
2	-15	2+(-15)=-13
3	-10	3+(-10)=-7
5	-6	5+(-6)=-1
-1	30	-1+30=29
-2	15	-2+15=13
-3	10	-3+10=7
-5	6	-5+6=1

From this list we can see that 5 and -6 add up to -1 and multiply to -30

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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