  We study the hadronic D meson decays into a pseudoscalar meson $P$ and an
even-parity meson $M$, where $M$ represents a scalar meson $S$, an axial-vector
meson $A$, or a tensor meson $T$. These decays are first analyzed in the
flavor-diagram approach. Fits to the $SP$ modes with $S$ being a non-strange
scalar meson show that neither the simple $q\bar q$ picture nor the $q^2\bar
q^2$ scheme is favored by data. Current measurements on the $AP$ decays are
insufficient for a meaningful analysis. Some $TP$ data are inconsistent with
the others. In certain cases, the $W$-annihilation diagrams indicated by the
data are unexpectedly large. As a comparison, we also compute their decay rates
in the factorization approach using form factors extracted from the covariant
light-front model. We find that factorization works well for Cabibbo-allowed
$D^+ \to SP,AP$ decays free of the weak annihilation contributions
($W$-exchange or $W$-annihilation). For the other $SP$ and $AP$ modes, it is
necessary to include weak annihilation contributions to account for the data.
However, factoriztion fails for $D\to TP$ decays for some unknown reason; the
predicted rates are in general too small by at least two orders of magnitude
compared to experiment. We also examine the finite width effects of resonances.
Some decay modes which are kinematically forbidden become physically allowed
due to the finite width of the resonance. We show that the branching fraction
of $D^+\to\sigma\pi^+$ extracted from three-body decays is enhanced by a factor
of 2, whereas $\B(D^0\to f_2(1270)\ov K^0)$ is reduced by a factor of 4 by
finite width effects.
