SOLUTION: Factoring Trinomials by Trial and Error 18x^3y+36x^2y-32xy

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Question 57403: Factoring Trinomials by Trial and Error
18x^3y+36x^2y-32xy
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
18x^3y + 36x^2y - 32xy
2xy(9x^2 + 18x - 16)
2xy(9x^2 + 18x - 16)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B18x%2B-16+=+0) has the following solutons:

x%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=%2818%29%5E2-4%2A9%2A-16=900.

Discriminant d=900 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-18%2B-sqrt%28+900+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2818%29%2Bsqrt%28+900+%29%29%2F2%5C9+=+0.666666666666667
x%5B2%5D+=+%28-%2818%29-sqrt%28+900+%29%29%2F2%5C9+=+-2.66666666666667

Quadratic expression 9x%5E2%2B18x%2B-16 can be factored:
9x%5E2%2B18x%2B-16+=+9%28x-0.666666666666667%29%2A%28x--2.66666666666667%29
Again, the answer is: 0.666666666666667, -2.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B18%2Ax%2B-16+%29