Question 604356: Can 5x^2 + 2x - 13 = 0 be factored?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
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 :
1,5,13,65
-1,-5,-13,-65
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-65) = -65
5*(-13) = -65
(-1)*(65) = -65
(-5)*(13) = -65
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 | -65 | 1+(-65)=-64 | | 5 | -13 | 5+(-13)=-8 | | -1 | 65 | -1+65=64 | | -5 | 13 | -5+13=8 |
From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.
This tells us that is prime.
This means that you'll have to either complete the square or use the quadratic formula to solve the given equation.
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