Give examples of polynomials p(x),
Question.

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.


Solution:

(i) $p(x)=2 x^{2}+2 x+8, g(x)=2 x^{0}=2$

$q(x)=x^{2}+x+4 ; r(x)=0$

(ii) $\mathrm{p}(\mathrm{x})=2 \mathrm{x}^{2}+2 \mathrm{x}+8 ; \mathrm{g}(\mathrm{x})=\mathrm{x}^{2}+\mathrm{x}+9$;

$q(x)=2 ; r(x)=-10$

(iii) $\mathrm{p}(\mathrm{x})=\mathrm{x}^{3}+\mathrm{x}+5 ; \mathrm{g}(\mathrm{x})=\mathrm{x}^{2}+1 ;$

$\mathrm{q}(\mathrm{x})=\mathrm{x} ; \mathrm{r}(\mathrm{x})=5$
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