Question 133695: Solve each equation by factoring.
-2x^2-7x-15=0
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let's see if we can factor 
Looking at we can see that the first term is  and the last term is  where the coefficients are -2 and -15 respectively.
Now multiply the first coefficient -2 and the last coefficient -15 to get 30. Now what two numbers multiply to 30 and add to the middle coefficient -7? 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 two negative numbers multiplied together make a positive number
Now which of these pairs add to -7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -7
| First Number | Second Number | Sum | | 1 | 30 | 1+30=31 | | 2 | 15 | 2+15=17 | | 3 | 10 | 3+10=13 | | 5 | 6 | 5+6=11 | | -1 | -30 | -1+(-30)=-31 | | -2 | -15 | -2+(-15)=-17 | | -3 | -10 | -3+(-10)=-13 | | -5 | -6 | -5+(-6)=-11 |
None of these pairs of factors add to -7. So the expression cannot be factored
So make sure that you copied the problem down correctly
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