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

Dear student,p(x)=g(x)×q(x)+rx(i) deg p(x)=deg q(x)let q(x)=x2; g(x)=2; r=x2p(x)=2×x2+x2=3x2(ii) deg q(x)= deg r(x)let q(x)=x2; g(x)=2; r=x2p(x)=2×x2+x2=3x2(iii) deg r(x)=0 means r(x) is a constantLet, q(x)=x2; g(x)=2; r(x)=2p(x)=2×x2+2=2x2+2Regards

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