  Suppose the knot group G(K) of a knot K has a non-abelian representation \rho
on A_4 \subset GL(4,Z). We conjecture that the twisted Alexander polynomial of
K associated to \rho is of the form: \Delta_K(t)/(1-t) \phi(t^3), where
\Delta_K (t) is the Alexander polynomial of K and \phi(t^3) is an integer
polynomial in t^3. We prove the conjecture for 2-bridge knots K whose group
G(K) can be mapped onto a free product Z/2*Z/3. Later, we discuss more general
metabelian representations of the knot groups and propose a similar conjecture
on the form of the twisted Alexander polynomials.
