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

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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) About Me  (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 1x%5E2-2xy-15y%5E2 we can see that the first term is 1x%5E2 and the last term is -15y%5E2 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 NumberSecond NumberSum
1-151+(-15)=-14
3-53+(-5)=-2
-115-1+15=14
-35-3+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 1x%5E2-2xy-15y%5E2, replace -2xy with 3xy%2B-5xy (notice 3xy%2B-5xy adds up to -2xy. So it is equivalent to -2xy)

1x%5E2%2Bhighlight%283xy%2B-5xy%29%2B-15y%5E2


Now let's factor 1x%5E2%2B3xy-5xy-15y%5E2 by grouping:


%281x%5E2%2B3xy%29%2B%28-5xy-15y%5E2%29 Group like terms


x%28x%2B3y%29-5y%28x%2B3y%29 Factor out the GCF of x out of the first group. Factor out the GCF of -5y out of the second group


%28x-5y%29%28x%2B3y%29 Since we have a common term of x%2B3y, we can combine like terms

So 1x%5E2%2B3xy-5xy-15y%5E2 factors to %28x-5y%29%28x%2B3y%29


So this also means that 1x%5E2-2xy-15y%5E2 factors to %28x-5y%29%28x%2B3y%29 (since 1x%5E2-2xy-15y%5E2 is equivalent to 1x%5E2%2B3xy-5xy-15y%5E2)



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Answer:
So x%5E2-2xy-15y%5E2 factors to %28x-5y%29%28x%2B3y%29






# 2

Looking at x%5E2%2Bx%2B1 we can see that the first term is x%5E2 and the last term is 1 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 NumberSecond NumberSum
111+1=2
-1-1-1+(-1)=-2

None of these pairs of factors add to 1. So the expression x%5E2%2Bx%2B1 cannot be factored