Draft:Bpow59

Describe as explicitly as you can all cubic polynomials with integer coefficients having

1. three distinct real roots,
2. local maximum and minimum values at integers, and
3. point of inflection at an integer.

An example of such a polynomial is <m>2x^3 - 18x^2 + 30x + 23</m>.

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.