How can you completely factor the following polynomial:

Question

6x^5-51x^3-27x

Answer 1

clearly the 1st step is to factor out 3x:

3x(2x^4-17x^2-9)

Then you have a quadratic in x^2, which you can factor with a little work, to get

3x(x^2-9)(2x^2+1)

The x^2-9 is easy, giving

3x(x-3)(x+3)(2x^2+1)