SOLUTION: x^2-2xy-15y^2 x^2+x+1 5x^2+25x+30 x^2-xy-12y^2

Question 143549: x^2-2xy-15y^2
x^2+x+1
5x^2+25x+30
x^2-xy-12y^2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Do you want to factor?

I'll do the first two to get you started

# 1

Looking at we can see that the first term is and the last term is where the coefficients are 1 and -15 respectively.

Now multiply the first coefficient 1 and the last coefficient -15 to get -15. Now what two numbers multiply to -15 and add to the middle coefficient -2? Let's list all of the factors of -15:

Factors of -15:
1,3,5,15

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

These factors pair up and multiply to -15
(1)*(-15)
(3)*(-5)
(-1)*(15)
(-3)*(5)

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

Now which of these pairs add to -2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -2

First Number	Second Number	Sum
1	-15	1+(-15)=-14
3	-5	3+(-5)=-2
-1	15	-1+15=14
-3	5	-3+5=2

From this list we can see that 3 and -5 add up to -2 and multiply to -15

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 )

------------------------------------------------------------

Answer:
So factors to

# 2

Looking at we can see that the first term is and the last term is where the coefficients are 1 and 1 respectively.

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

Factors of 1:
1

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

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

note: remember two negative numbers multiplied together make a positive 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	1	1+1=2
-1	-1	-1+(-1)=-2

None of these pairs of factors add to 1. So the expression cannot be factored

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