SOLUTION: -9x^2+81x+180 factor completely

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Question 660583: -9x^2+81x+180 factor completely
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-9x%5E2%2B81x%2B180 Start with the given expression.


-9%28x%5E2-9x-20%29 Factor out the GCF -9.


Now let's try to factor the inner expression x%5E2-9x-20


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Looking at the expression x%5E2-9x-20, we can see that the first coefficient is 1, the second coefficient is -9, and the last term is -20.


Now multiply the first coefficient 1 by the last term -20 to get %281%29%28-20%29=-20.


Now the question is: what two whole numbers multiply to -20 (the previous product) and add to the second coefficient -9?


To find these two numbers, we need to list all of the factors of -20 (the previous product).


Factors of -20:
1,2,4,5,10,20
-1,-2,-4,-5,-10,-20


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


These factors pair up and multiply to -20.
1*(-20) = -20
2*(-10) = -20
4*(-5) = -20
(-1)*(20) = -20
(-2)*(10) = -20
(-4)*(5) = -20

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -9:


First NumberSecond NumberSum
1-201+(-20)=-19
2-102+(-10)=-8
4-54+(-5)=-1
-120-1+20=19
-210-2+10=8
-45-4+5=1



From the table, we can see that there are no pairs of numbers which add to -9. So x%5E2-9x-20 cannot be factored.


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Answer:


So -9x%5E2%2B81x%2B180 simply factors to -9%28x%5E2-9x-20%29


In other words, -9x%5E2%2B81x%2B180=-9%28x%5E2-9x-20%29.