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Sample Question 24:
Let \(P(x) = (x - 1)(x - 2)(x - 3)\). For how many polynomials \(Q(x)\) does there exist a polynomial \(R(x)\) of degree 3 such that \(P(Q(x)) = P(x) \cdot R(x)\)?
\(\mathrm {(A) } 19 \qquad \mathrm {(B) } 22 \qquad \mathrm {(C) } 24 \qquad \mathrm {(D) } 27 \qquad \mathrm {(E) } 32\)