SOLUTION: Factor the polynomial. Please explain and solve: 32n (n is to the second power) - 80n +50

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Question 5115: Factor the polynomial. Please explain and solve:
32n (n is to the second power) - 80n +50
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
32n%5E2-80n%2B50
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation an%5E2%2Bbn%2Bc=0 (in our case 32n%5E2%2B-80n%2B50+=+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=%28-80%29%5E2-4%2A32%2A50=0.

Discriminant d=0 is zero! That means that there is only one solution: n+=+%28-%28-80%29%29%2F2%5C32.
Expression can be factored: 32n%5E2%2B-80n%2B50+=+32%28n-1.25%29%2A%28n-1.25%29

Again, the answer is: 1.25, 1.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+32%2Ax%5E2%2B-80%2Ax%2B50+%29