Question

On dividing a polynomial p(x) by a non-zero polynomial q(x), let g(x) be the quotient and r(x) be the remainder, than p(x) = q(x)⋅g(x) + r(x), where

(a) r(x) = 0 always
(b) deg r (x) <deg g(x) always
(c) either r(x) = 0 or deg r(x) <deg g(x)
(d) r(x) = g(x)

Answer 1

$$\begin{gathered} \left(\mathrm{c}\right)\mathrm{either}r\left(x\right)=0or\mathrm{deg}r\left(x\right)<\mathrm{deg}g\left(x\right) \\ \text{By division algorithm on polynomials, either}r\left(x\right)=0\text{or deg}r\left(x\right)<\text{deg}g\left(x\right). \end{gathered}$$