SOLUTION: How do you factor 3x^3-30x-15x^2? Could you please show and explain each step? Thank you so much.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you factor 3x^3-30x-15x^2? Could you please show and explain each step? Thank you so much.      Log On


   

Question 50552: How do you factor 3x^3-30x-15x^2? Could you please show and explain
each step? Thank you so much.
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
3x^3 - 15x^2 - 30x
x(3x^2 - 15x - 30)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-15x%2B-30+=+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=%28-15%29%5E2-4%2A3%2A-30=585.

Discriminant d=585 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--15%2B-sqrt%28+585+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-15%29%2Bsqrt%28+585+%29%29%2F2%5C3+=+6.53112887414927
x%5B2%5D+=+%28-%28-15%29-sqrt%28+585+%29%29%2F2%5C3+=+-1.53112887414927

Quadratic expression 3x%5E2%2B-15x%2B-30 can be factored:
3x%5E2%2B-15x%2B-30+=+3%28x-6.53112887414927%29%2A%28x--1.53112887414927%29
Again, the answer is: 6.53112887414927, -1.53112887414927. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-15%2Ax%2B-30+%29