2003 AMC 12A Problem 21

Since $(0,0)$ is an intercept, $P(0)=e=0,$ so $P(x)$ $=x\left(x^4+ax^3+bx^2+cx+d\right).$ The four remaining intercepts are nonzero and distinct, and $d$ equals their product, which is therefore nonzero. Any of $a,b,c$ can be zero for suitable choices of those roots, but $d\neq0.$ Thus, the correct answer is D.