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, then 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

(c) either r(x) = 0 or deg r(x) ˂ deg g(x) 

By division algorithm on polynomials, 

either r(x) = 0 or deg r(x) ˂ deg g(x).