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Sagot :
Let's begin dividing the leading term of the dividend by the leading term of the divisor
[tex]\frac{x^3}{x}=x^2[/tex]Multiply it by the divisor
[tex]x^2\left(x−9\right)=x^3−9x^2[/tex]Subtract the dividend from the obtained result
[tex]\left(x^3−734\right)−\left(x^3−9x^2\right)=9x^2−734[/tex]Divide the leading term of the obtained remainder by the leading term of the divisor
[tex]\frac{9x^2}{x}=9x[/tex]Multiply it by the divisor
[tex]9x\left(x−9\right)=9x^2−81x[/tex]Subtract the remainder from the obtained result
[tex]\left(9x^2−734\right)−\left(9x^2−81x\right)=81x−734.[/tex]Divide the leading term of the obtained remainder by the leading term of the divisor
[tex]\frac{81x}{x}=81[/tex]Multiply it by the divisor
[tex]81\left(x−9\right)=81x−729[/tex]Subtract the remainder from the obtained result
[tex]\left(81x−734\right)−\left(81x−729\right)=−5[/tex]since the degree of the remainder is less than the degree of the divisor, then we are done
[tex]x^2+9x+81+−\frac{5}{x−9}[/tex]The quotient is
[tex]\begin{equation*} x^2+9x+81 \end{equation*}[/tex]The remainder is
[tex]-5[/tex]
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