Question 302560: 6x^5-11x^4+30x^3
Thank you very much for your help, I need to factor completly.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
 Start with the given expression.
 Factor out the GCF  .
Now let's try to factor the inner expression 
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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 :
1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
-1,-2,-3,-4,-5,-6,-9,-10,-12,-15,-18,-20,-30,-36,-45,-60,-90,-180
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*180 = 180
2*90 = 180
3*60 = 180
4*45 = 180
5*36 = 180
6*30 = 180
9*20 = 180
10*18 = 180
12*15 = 180
(-1)*(-180) = 180
(-2)*(-90) = 180
(-3)*(-60) = 180
(-4)*(-45) = 180
(-5)*(-36) = 180
(-6)*(-30) = 180
(-9)*(-20) = 180
(-10)*(-18) = 180
(-12)*(-15) = 180
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 | 180 | 1+180=181 | | 2 | 90 | 2+90=92 | | 3 | 60 | 3+60=63 | | 4 | 45 | 4+45=49 | | 5 | 36 | 5+36=41 | | 6 | 30 | 6+30=36 | | 9 | 20 | 9+20=29 | | 10 | 18 | 10+18=28 | | 12 | 15 | 12+15=27 | | -1 | -180 | -1+(-180)=-181 | | -2 | -90 | -2+(-90)=-92 | | -3 | -60 | -3+(-60)=-63 | | -4 | -45 | -4+(-45)=-49 | | -5 | -36 | -5+(-36)=-41 | | -6 | -30 | -6+(-30)=-36 | | -9 | -20 | -9+(-20)=-29 | | -10 | -18 | -10+(-18)=-28 | | -12 | -15 | -12+(-15)=-27 |
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 simply factors to
In other words,  .
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