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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.
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Answer:
So doesn't factor at all (over the rational numbers).
So is prime.
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