Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and
(i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg r(x) = 0

(i) p(x) = \(2x^2 + 2x + 8\)
=>q(x) = \(x^2 + x + 4\)
=> g(x) = \(2\) and r(x) = \(0\)

(ii) p(x) = \(x^3 + x^2 + x + 1\)
=>q(x) = \(x + 1\)
=> g(x) = \(x^2 - 1\) and r(x) = \(2x + 2\)

(iii) p(x) = \(x^3 - x^2 + 2x + 3\)
=>q(x) = \(x^2 + 2\)
=> g(x) = \(x - 1\) and r(x) = \(5\)