Question 708894: how to factor? -2x^2-3x+6
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
 Start with the given expression.
 Factor out the GCF  .
Now let's try to factor the inner expression 
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Looking at the expression , we can see that the first coefficient is  , the second coefficient is  , and the last term is  .
Now multiply the first coefficient by the last term to get  .
Now the question is: what two whole numbers multiply to  (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-12) = -12
2*(-6) = -12
3*(-4) = -12
(-1)*(12) = -12
(-2)*(6) = -12
(-3)*(4) = -12
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| First Number | Second Number | Sum | | 1 | -12 | 1+(-12)=-11 | | 2 | -6 | 2+(-6)=-4 | | 3 | -4 | 3+(-4)=-1 | | -1 | 12 | -1+12=11 | | -2 | 6 | -2+6=4 | | -3 | 4 | -3+4=1 |
From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.
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Answer:
So simply factors to
In other words,  .
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