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