I don't feel like doing long division right now, so let's just try some values.

a) If x = 0, then we have p divides 30

b) If x = 1, then we have p+3 divides 66

c) If x = -1, then we have p-3 divides 0

(unless I have done the math wrong)

(c) provides no information.

(a) means that p is either 1,2,3,5, 6, 10,15, 30, -1, -2, -3,-5, -6, -10, -15 or -30.

But p+3 must divide 66, so the only viable candidates are 3, 30, -2 and -6.

Well, that's encouraging. Let's try a few more values.

d) If x = 2, then we have p+12 divides 5280

e) If x = -2, then we have p-4 divides 9108

(more opportunities for math errors)

Based on (d), we can eliminate p = 30

Based on (e), we can eliminate p = -6

So the only viable candidates are p = 3 and p = -2.

Of course, I haven't proven that either one works for all x.

But the long division is more viable now. Perhaps I'll finish it off after grocery shopping.

*Edited on ***February 15, 2015, 11:09 am**