The preimage $\preimage{T}{0}$ is the set of all polynomials $a + bx + cx^2 + dx^3$ so that
$\lt{T}{a + bx + cx^2 + dx^3} = 0$. Thus, $b + 2cx + 3dx^2 = 0$, where the $0$ represents the zero polynomial. In order to satisfy this equation, we must have $b = 0$, $c = 0$, and $d = 0$. Thus, $\preimage{T}{0}$ is precisely the set of all constant polynomials – polynomials of degree 0. Symbolically, this is $\preimage{T}{0} = \setparts{a}{a\in\complexes}$.
Does this seem familiar? What other operation sends constant functions to 0?