SOLUTION: How would I factor this: x^2 y^2 + 17xy -11

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Question 970513: How would I factor this:
x^2 y^2 + 17xy -11
Found 2 solutions by Alan3354, macston:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It's not possible.
It's prime

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
x%5E2y%5E2%2B17xy-11=0
Let N=xy
N%5E2%2B17N-11=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aN%5E2%2BbN%2Bc=0 (in our case 1N%5E2%2B17N%2B-11+=+0) has the following solutons:

N%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2817%29%5E2-4%2A1%2A-11=333.

Discriminant d=333 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-17%2B-sqrt%28+333+%29%29%2F2%5Ca.

N%5B1%5D+=+%28-%2817%29%2Bsqrt%28+333+%29%29%2F2%5C1+=+0.624143795447329
N%5B2%5D+=+%28-%2817%29-sqrt%28+333+%29%29%2F2%5C1+=+-17.6241437954473

Quadratic expression 1N%5E2%2B17N%2B-11 can be factored:
1N%5E2%2B17N%2B-11+=+1%28N-0.624143795447329%29%2A%28N--17.6241437954473%29
Again, the answer is: 0.624143795447329, -17.6241437954473. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B17%2Ax%2B-11+%29

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%28N-0.624%29%28N%2B17.624%29=0 Replace N with xy
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ANSWER: (xy-0.624)(xy+17.624)=0