Question 180801: X^2 + 3x -15
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Do you want to factor?
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 :
1,3,5,15
-1,-3,-5,-15
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-15)
3*(-5)
(-1)*(15)
(-3)*(5)
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 | -15 | 1+(-15)=-14 | | 3 | -5 | 3+(-5)=-2 | | -1 | 15 | -1+15=14 | | -3 | 5 | -3+5=2 |
From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.
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