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

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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