2018 AMC 12B Problem 22

Consider polynomials P(x) of degree at most 3, each of whose coefficients is an element of \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}. How many such polynomials satisfy P(-1) = -9?

\textbf{(A) } 110 \qquad \textbf{(B) } 143 \qquad \textbf{(C) } 165 \qquad \textbf{(D) } 220 \qquad \textbf{(E) } 286

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.