Question

give examples of polynomias p(x),q(x),g(x),r(x) which satisfy the division algorithm and deg r(x)=0

Answer 1

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm(i)deg p(x) = deg q(x)  (ii) deg q(x) = deg r(x) And (iii) deg r(x) = 0We can write  many such examples(i)deg p(x) = deg q(x)We can write  many such examplesP(x)  = x2   , q(x) = x2  g(x) = 1 R(x) = 0
(ii) deg q(x) = deg r(x)Q(x) = x , R(x) = x , p(x) = x2 + x   g(x) = x2
(iii) deg r(x) = 0Q(x) = 1 , R(x) = 1 , p(x) = x+1, g(x) = x