SOLUTION: factor completely. 9x^7-45x^6+18x^5

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Question 578009: factor completely.
9x^7-45x^6+18x^5
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
-1,-2

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*2 = 2
(-1)*(-2) = 2

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 2 1+2=3
-1 -2 -1+(-2)=-3

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, .