Question 222684: Factor completely. 7x^7-56x^6+28x^5
Thanks!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
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 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 :
1,2,4
-1,-2,-4
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*4 = 4
2*2 = 4
(-1)*(-4) = 4
(-2)*(-2) = 4
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 | 4 | 1+4=5 | | 2 | 2 | 2+2=4 | | -1 | -4 | -1+(-4)=-5 | | -2 | -2 | -2+(-2)=-4 |
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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