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 :
1,5,17,25,85,425
-1,-5,-17,-25,-85,-425
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-425) = -425
5*(-85) = -425
17*(-25) = -425
(-1)*(425) = -425
(-5)*(85) = -425
(-17)*(25) = -425
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 | -425 | 1+(-425)=-424 | | 5 | -85 | 5+(-85)=-80 | | 17 | -25 | 17+(-25)=-8 | | -1 | 425 | -1+425=424 | | -5 | 85 | -5+85=80 | | -17 | 25 | -17+25=8 |
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.
|
(