SOLUTION: factor or grouping 3x^2+15x+25

Question 299602: factor or grouping
3x^2+15x+25
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 :
1,3,5,15,25,75
-1,-3,-5,-15,-25,-75

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

These factors pair up and multiply to .
1*75 = 75
3*25 = 75
5*15 = 75
(-1)*(-75) = 75
(-3)*(-25) = 75
(-5)*(-15) = 75

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	75	1+75=76
3	25	3+25=28
5	15	5+15=20
-1	-75	-1+(-75)=-76
-3	-25	-3+(-25)=-28
-5	-15	-5+(-15)=-20

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

===============================================================

Answer:

So doesn't factor at all (over the rational numbers).

So is prime.

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