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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
:
1,2,3,6,9,18
-1,-2,-3,-6,-9,-18
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to
.
1*18
2*9
3*6
(-1)*(-18)
(-2)*(-9)
(-3)*(-6)
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 | 18 | 1+18=19 |
| 2 | 9 | 2+9=11 |
| 3 | 6 | 3+6=9 |
| -1 | -18 | -1+(-18)=-19 |
| -2 | -9 | -2+(-9)=-11 |
| -3 | -6 | -3+(-6)=-9 |
From the table, we can see that there are no pairs of numbers which add to
. So
cannot be factored.
So
is prime.
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