Question 538903: Please help me factor 
I know that the first number in the bracket will probably have to be 9 or 3 but I'm not sure about how about the other numbers since 89 and 40 do not have a common multiple.
Thanks!
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 :
1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
-1,-2,-3,-4,-5,-6,-8,-9,-10,-12,-15,-18,-20,-24,-30,-36,-40,-45,-60,-72,-90,-120,-180,-360
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*360 = 360
2*180 = 360
3*120 = 360
4*90 = 360
5*72 = 360
6*60 = 360
8*45 = 360
9*40 = 360
10*36 = 360
12*30 = 360
15*24 = 360
18*20 = 360
(-1)*(-360) = 360
(-2)*(-180) = 360
(-3)*(-120) = 360
(-4)*(-90) = 360
(-5)*(-72) = 360
(-6)*(-60) = 360
(-8)*(-45) = 360
(-9)*(-40) = 360
(-10)*(-36) = 360
(-12)*(-30) = 360
(-15)*(-24) = 360
(-18)*(-20) = 360
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 | 360 | 1+360=361 | | 2 | 180 | 2+180=182 | | 3 | 120 | 3+120=123 | | 4 | 90 | 4+90=94 | | 5 | 72 | 5+72=77 | | 6 | 60 | 6+60=66 | | 8 | 45 | 8+45=53 | | 9 | 40 | 9+40=49 | | 10 | 36 | 10+36=46 | | 12 | 30 | 12+30=42 | | 15 | 24 | 15+24=39 | | 18 | 20 | 18+20=38 | | -1 | -360 | -1+(-360)=-361 | | -2 | -180 | -2+(-180)=-182 | | -3 | -120 | -3+(-120)=-123 | | -4 | -90 | -4+(-90)=-94 | | -5 | -72 | -5+(-72)=-77 | | -6 | -60 | -6+(-60)=-66 | | -8 | -45 | -8+(-45)=-53 | | -9 | -40 | -9+(-40)=-49 | | -10 | -36 | -10+(-36)=-46 | | -12 | -30 | -12+(-30)=-42 | | -15 | -24 | -15+(-24)=-39 | | -18 | -20 | -18+(-20)=-38 |
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.
If you need more help, email me at jim_thompson5910@hotmail.com
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Jim
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