Question 581889: I need help factoring this trinomial: 8k^2-9k+9
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 :
1,2,3,4,6,8,9,12,18,24,36,72
-1,-2,-3,-4,-6,-8,-9,-12,-18,-24,-36,-72
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*72 = 72
2*36 = 72
3*24 = 72
4*18 = 72
6*12 = 72
8*9 = 72
(-1)*(-72) = 72
(-2)*(-36) = 72
(-3)*(-24) = 72
(-4)*(-18) = 72
(-6)*(-12) = 72
(-8)*(-9) = 72
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 | 72 | 1+72=73 | | 2 | 36 | 2+36=38 | | 3 | 24 | 3+24=27 | | 4 | 18 | 4+18=22 | | 6 | 12 | 6+12=18 | | 8 | 9 | 8+9=17 | | -1 | -72 | -1+(-72)=-73 | | -2 | -36 | -2+(-36)=-38 | | -3 | -24 | -3+(-24)=-27 | | -4 | -18 | -4+(-18)=-22 | | -6 | -12 | -6+(-12)=-18 | | -8 | -9 | -8+(-9)=-17 |
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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