The cubic polynomial 6x3−30x2+24x arises in a physics experiment while simplifying an algebraic expression for force. Analyse it as follows:
a. (i) Factorise the polynomial completely.
b. (ii) Hence, determine all values of x for which the polynomial is zero.
c. (iii) Show that the product of the non-zero roots is equal to the constant term of the quadratic factor obtained after the first stage of factorisation.