SOLUTION: Factor the following expression completely: 45y3 – 33y2 + 6y

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Question 547708: Factor the following expression completely:
45y3 – 33y2 + 6y

Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
3y is incommon with all 3 variables
3y%2812y%5E2-11y%2B2%29
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 12y%5E2%2B-11y%2B2+=+0) has the following solutons:

y%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=%28-11%29%5E2-4%2A12%2A2=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--11%2B-sqrt%28+25+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+25+%29%29%2F2%5C12+=+0.666666666666667
y%5B2%5D+=+%28-%28-11%29-sqrt%28+25+%29%29%2F2%5C12+=+0.25

Quadratic expression 12y%5E2%2B-11y%2B2 can be factored:
12y%5E2%2B-11y%2B2+=+12%28y-0.666666666666667%29%2A%28y-0.25%29
Again, the answer is: 0.666666666666667, 0.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B-11%2Ax%2B2+%29

16%2F24=2%2F3
6%2F24=1%2F4
3y%28y-%282%2F3%29%29%28y-%281%2F4%29%29