Hi, I am stuck at this question. Appreciate if you could guide or help to solve this. Your thoughts would be greatly appreciated. Thanks!

Find the remainder when f(x)=(x^4 - x^3 + 2x - 3) g(x) is divided by x-3, given that x-3 is a factor of g(x)+3, where g(x) is a polynomial.

Hint: Say p(x) = (x-s)q(x) + r(x), where deg(r) < deg(x-s) = 1, which would mean that r(x) is a constant, say r0, so p(x) = (x-s)q(x) + r0.
Then, p(s) = 0*q(s) + r0 = r0, is the remainder.