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

Answer 1

$$\begin{gathered} Dearstudent, \\ p\left(x\right)=g\left(x\right)\times q\left(x\right)+r\left(x\right) \\ \left(i\right)degp\left(x\right)=degq\left(x\right) \\ letq\left(x\right)=x^2;g\left(x\right)=2;r=x^2 \\ p\left(x\right)=2\times x^2+x^2=3x^2 \\ \left(ii\right)degq\left(x\right)=degr\left(x\right) \\ letq\left(x\right)=x^2;g\left(x\right)=2;r=x^2 \\ p\left(x\right)=2\times x^2+x^2=3x^2 \\ \left(iii\right)degr\left(x\right)=0meansr\left(x\right)isacons\tan t \\ Let,q\left(x\right)=x^2;g\left(x\right)=2;r\left(x\right)=2 \\ p\left(x\right)=2\times x^2+2=2x^2+2 \\ Regards \end{gathered}$$