A polynomial $p(x)$ gives a remainder of $1$ when divided by $x^{100}$ and a remainder of $2$ when divided by $(x-2)^3$. Evaluate $p(x)$.
By the Remainder Theorem, $p(x)$ can be written as $$p(x) =x^{100}\times h(x)+1 = (x-2)^3 \times g(x) +2 $$
for some polynomials $f(x)$ and $g(x)$, but how do I solve further?
Any help will be appreciated.
Thanks.