Problem  of the  Week

Note: Because of Spring Break, this Problem of the Week will remain posted for two weeks.

Describe as explicitly as you can all cubic polynomials with integer coefficients having
(a) three distinct real roots,
(b) local maximum and minimum values at integers, and
(c) point of inflection at an integer.

An example of such a polynomial is 2x³ - 18x² + 30x + 23.

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