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

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

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) (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 :
1,3
-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 .
1*(-3)
(-1)*(3)

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	-3	1+(-3)=-2
-1	3	-1+3=2

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored. This means that the polynomial is prime.

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