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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
:
1,2,3,4,6,9,12,18,36
-1,-2,-3,-4,-6,-9,-12,-18,-36
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to
.
1*36 = 36
2*18 = 36
3*12 = 36
4*9 = 36
6*6 = 36
(-1)*(-36) = 36
(-2)*(-18) = 36
(-3)*(-12) = 36
(-4)*(-9) = 36
(-6)*(-6) = 36
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 | 36 | 1+36=37 |
| 2 | 18 | 2+18=20 |
| 3 | 12 | 3+12=15 |
| 4 | 9 | 4+9=13 |
| 6 | 6 | 6+6=12 |
| -1 | -36 | -1+(-36)=-37 |
| -2 | -18 | -2+(-18)=-20 |
| -3 | -12 | -3+(-12)=-15 |
| -4 | -9 | -4+(-9)=-13 |
| -6 | -6 | -6+(-6)=-12 |
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.
If you need more help, email me at jim_thompson5910@hotmail.com
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Jim
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