Question

give examples of polynomials p(x),q(X) and r(X),which satisfy the division algorithm and (A) deg p(x)=deg q(x)
(B)deg q(x)=deg r(x)
(C) deg r(x)=0

Answer 1

We can write  many such examples

(i)deg p(x) = deg q(x)
P(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) = 0
Q(x) = 1 , R(x) = 1 , p(x) = x+1, g(x) = x

Answer 2

1. P(x)=2x^2-2x+14,g(x)=2,q(x)=x^2-x+7,r=0
2.p(x)=x^3+2x^2+x+1,g(x)=x^2-1,q=x+1,r(x)=2x+2
3.p(x)=x^3+2x^2-x+2,g(x)=x^2-1,q(x)=x+2,r(x)=4