Well, once you know that p = 3 or p = -2, the factoring is fairly easy.
x12 - x11 + 3x10 + 11x3 - x2 + 23x + 30 =
(x3 + 2x + 3) *
(x^9 - x^8 + x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x + 10)
But x3 + 2x -2 does not divide evenly into the expression
So, the only solution is p = 3
Edited on February 14, 2015, 7:55 pm