Well, once you know that p = 3 or p = -2, the factoring is fairly easy.

x^{12} - x^{11} + 3x^{10} + 11x^{3} - x^{2} + 23x + 30 =

(x^{3} + 2x + 3) *

(x^9 - x^8 + x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x + 10)

But x^{3} + 2x -2 does not divide evenly into the expression

**So, the only solution is p = 3**

*Edited on ***February 14, 2015, 7:55 pm**