SOLUTION: Can 5x^2 + 2x - 13 = 0 be factored?

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Question 604356: Can 5x^2 + 2x - 13 = 0 be factored?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 5x%5E2%2B2x-13, we can see that the first coefficient is 5, the second coefficient is 2, and the last term is -13.


Now multiply the first coefficient 5 by the last term -13 to get %285%29%28-13%29=-65.


Now the question is: what two whole numbers multiply to -65 (the previous product) and add to the second coefficient 2?


To find these two numbers, we need to list all of the factors of -65 (the previous product).


Factors of -65:
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 -65.
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 2:


First NumberSecond NumberSum
1-651+(-65)=-64
5-135+(-13)=-8
-165-1+65=64
-513-5+13=8



From the table, we can see that there are no pairs of numbers which add to 2. So 5x%5E2%2B2x-13 cannot be factored.


This tells us that 5x%5E2%2B2x-13 is prime.


This means that you'll have to either complete the square or use the quadratic formula to solve the given equation.