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

Algebra.Com's Answer #199421 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
You're off to a great start, I'll show you how to factor $\"17x%5E2%2B20x-25\"$ (if it's even possible).\r
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Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

Looking at the expression $\"17x%5E2%2B20x-25\"$ , we can see that the first coefficient is $\"17\"$ , the second coefficient is $\"20\"$ , and the last term is $\"-25\"$ .

Now multiply the first coefficient $\"17\"$ by the last term $\"-25\"$ to get $\"%2817%29%28-25%29=-425\"$ .

Now the question is: what two whole numbers multiply to $\"-425\"$ (the previous product) and add to the second coefficient $\"20\"$ ?

To find these two numbers, we need to list all of the factors of $\"-425\"$ (the previous product).

Factors of $\"-425\"$ :

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 $\"-425\"$ .

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 $\"20\"$ :

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First Number	Second Number	Sum
1	-425	1+(-425)=-424
5	-85	5+(-85)=-80
17	-25	17+(-25)=-8
-1	425	-1+425=424
-5	85	-5+85=80
-17	25	-17+25=8

From the table, we can see that there are no pairs of numbers which add to $\"20\"$ . So $\"17x%5E2%2B20x-25\"$ cannot be factored.

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Answer:

So $\"17%2Ax%5E2%2B20%2Ax-25\"$ doesn't factor at all (over the rational numbers).

So $\"17%2Ax%5E2%2B20%2Ax-25\"$ is prime.

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