SOLUTION: Factor the trinomial x^2-9xy-10y^2

Question 190252: Factor the trinomial
x^2-9xy-10y^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 -10 respectively.

Now multiply the first coefficient 1 and the last coefficient -10 to get -10. Now what two numbers multiply to -10 and add to the middle coefficient -9? Let's list all of the factors of -10:

Factors of -10:
1,2,5,10

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

These factors pair up and multiply to -10
(1)*(-10)
(2)*(-5)
(-1)*(10)
(-2)*(5)

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

Now which of these pairs add to -9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -9

First Number	Second Number	Sum
1	-10	1+(-10)=-9
2	-5	2+(-5)=-3
-1	10	-1+10=9
-2	5	-2+5=3

From this list we can see that 1 and -10 add up to -9 and multiply to -10

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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