SOLUTION: I need help factoring this trinomial: 8k^2-9k+9

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.

===============================================================

Answer:

So doesn't factor at all (over the rational numbers).

So is prime.

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