$\left. \begin{matrix}    g\left( x \right)=Q'\left( x \right)\left( {{x}^{2}}+2x+5 \right)+x  \\    f\left( x \right)=Q\left( x \right)\left( {{x}^{2}}+2x+5 \right)+\left( x-1 \right)  \\ \end{matrix} \right\}$  $\xrightarrow{x}f\left( x \right).g\left( x \right)=\left( {{x}^{2}}+2x+5 \right)\left( \left( {{x}^{2}}+2x+5 \right)Q'\left( x \right)Q\left( x \right)+\left( x-1 \right)Q'\left( x \right)+xQ\left( x \right) \right)+x\left( x-1 \right)$ $=\left( {{x}^{2}}+2x+5 \right)Q''\left( x \right)+\left( {{x}^{2}}-x  \right)$  لذا برای تعیین باقیمانده، کافیست $x\left( x-1 \right)$ را برای ${{x}^{2}}+2x+5$ تقسیم کنیم:  ${{x}^{2}}-x=\left( {{x}^{2}}+2x+5 \right)\underbrace{-3x-5}_{\begin{smallmatrix}   \\ \end{smallmatrix}}$