Question 616008: Factor. Remember to use the largest common factor and to check by multiplying. Factor out a negative factor if the first coefficient is negative.
-10t^5+15t^4+9t^3
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 :
1,2,3,5,6,9,10,15,18,30,45,90
-1,-2,-3,-5,-6,-9,-10,-15,-18,-30,-45,-90
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-90) = -90
2*(-45) = -90
3*(-30) = -90
5*(-18) = -90
6*(-15) = -90
9*(-10) = -90
(-1)*(90) = -90
(-2)*(45) = -90
(-3)*(30) = -90
(-5)*(18) = -90
(-6)*(15) = -90
(-9)*(10) = -90
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 | -90 | 1+(-90)=-89 | | 2 | -45 | 2+(-45)=-43 | | 3 | -30 | 3+(-30)=-27 | | 5 | -18 | 5+(-18)=-13 | | 6 | -15 | 6+(-15)=-9 | | 9 | -10 | 9+(-10)=-1 | | -1 | 90 | -1+90=89 | | -2 | 45 | -2+45=43 | | -3 | 30 | -3+30=27 | | -5 | 18 | -5+18=13 | | -6 | 15 | -6+15=9 | | -9 | 10 | -9+10=1 |
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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