SOLUTION: Can you help me - is this able to be factored out? -17x^2 - 20x+25?? What I have so far is take out -1 so the equation is -1 (17x^2 + 20x - 25) When I multiply 17 x 25 = 425

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Question 272841: Can you help me - is this able to be factored out? -17x^2 - 20x+25??
What I have so far is take out -1 so the equation is -1 (17x^2 + 20x - 25)
When I multiply 17 x 25 = 425 I am having a hard time finding multiples of 425 that equal 20. Is it factorable?

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
You're off to a great start, I'll show you how to factor (if it's even possible).


Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


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 :

1,5,17,25,85,425

-1,-5,-17,-25,-85,-425



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



These factors pair up and multiply to .

1*(-425) = -425
5*(-85) = -425
17*(-25) = -425
(-1)*(425) = -425
(-5)*(85) = -425
(-17)*(25) = -425


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



First NumberSecond NumberSum
1-4251+(-425)=-424
5-855+(-85)=-80
17-2517+(-25)=-8
-1425-1+425=424
-585-5+85=80
-1725-17+25=8




From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.



===============================================================





Answer:



So doesn't factor at all (over the rational numbers).



So is prime.


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