Question 588384: The factors of 2x^2+5x+7
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 :
1,2,7,14
-1,-2,-7,-14
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*14 = 14
2*7 = 14
(-1)*(-14) = 14
(-2)*(-7) = 14
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 | 14 | 1+14=15 | | 2 | 7 | 2+7=9 | | -1 | -14 | -1+(-14)=-15 | | -2 | -7 | -2+(-7)=-9 |
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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