I suppose you could use Descartes' rule of signs to find an approximation for thenumberof roots.

But you arereallyasking about the rational roots test, I think, which is a small expansion of the factor theorem.

You have to consider that some factors might be of the form , where 'k' refers to any of the factors of , by testing , as you would with the factor theorem. You should find that there are indeed more factors to this polynomial.