x^100 ≡ p + a(x-1) ≡ r mod (x-2)

x^100 ≡ p - r + a(x-1) mod (x-2)

x^100 = p - r + a(x-1) + b(x-2)

x^100 = p-r + ax - a + bx - 2b

x^100 = x(a+b) - R