One dividing a polynomial p(x) by a nonzero polynomial q(x), let g(x) be the quotient and r(x) be the remainder then p(x) = q(x) g(x) + r(x), where

As, we know that

According to the division algorithm on polynomials, we have

either r (x) = 0 or deg r (x) < deg g (x)

Hence, option C is correct