AMC 12B 2023 (Problem 14)

For how many ordered pairs

(a,b)

of integers does the polynomial

x^3 + ax^2 + bx + 6

have 3 distinct integer roots?

\text{(A)}\;5

\text{(B)}\;6

\text{(C)}\;8

\text{(D)}\;7

\text{(E)}\;4