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Question 423125: x^2+3xy+9y^2
Basically, what 2 numbers have a product of 9 and a sum of 3??
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 coefficient is  .
Now multiply the first coefficient by the last coefficient 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 :
1,3,9
-1,-3,-9
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*9 = 9
3*3 = 9
(-1)*(-9) = 9
(-3)*(-3) = 9
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 | 9 | 1+9=10 | | 3 | 3 | 3+3=6 | | -1 | -9 | -1+(-9)=-10 | | -3 | -3 | -3+(-3)=-6 |
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.
If you need more help, email me at jim_thompson5910@hotmail.com
Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you
Jim
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