SOLUTION: Determine whether or not if it can be factored. If not, then state it is prime. 3x^2 + 5x - 1

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Question 154511: Determine whether or not if it can be factored. If not, then state it is prime.
3x^2 + 5x - 1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 3x%5E2%2B5x-1, we can see that the first coefficient is 3, the second coefficient is 5, and the last term is -1.


Now multiply the first coefficient 3 by the last term -1 to get %283%29%28-1%29=-3.


Now the question is: what two whole numbers multiply to -3 (the previous product) and add to the second coefficient 5?


To find these two numbers, we need to list all of the factors of -3 (the previous product).


Factors of -3:
1,3
-1,-3


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to -3.
1*(-3)
(-1)*(3)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 5:


First NumberSecond NumberSum
1-31+(-3)=-2
-13-1+3=2



From the table, we can see that there are no pairs of numbers which add to 5. So 3x%5E2%2B5x-1 cannot be factored. This means that the polynomial is prime.