When y is set to zero, what are the intercepts for X? There should be three.

Yes, there should be three usually, but not always.



And this polynomial cannot be easily factorised... there are no simple exact solutions.

See for yourself:

The solutions are:
x = -1.04
x = 0.941
x = 3.76

All rounded to 3 significant figures.

Or maybe you inserted a mistake in your question?