SOLUTION: Factor completely. 7x^7-56x^6+28x^5 Thanks!

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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