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# 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) = $$5$$