Polynomials, Cubic Equations and Partial Fractions

The polynomial \( P (x) = x^3 + ax^2 + bx + c\) is exactly divisible by \(x^2 - 5x + 6\).
Given that the remainder when \( P(x) \) is divided by \(x + 1\) is \(18\), find \(a, b, c\)