第7章 7.6 | 高専の数学解説

(1)

\begin{array}{r} x^{3}\phantom{0000}+2x\phantom{00}-1\phantom{0000000000}\\ x-1{\overline{\big)\;x^{4}-x^{3}+2x^{2}-3x+6\phantom{00}}}\\ \underline{x^{4}-x^{3}\phantom{+2x^{2}-3x+6\phantom{00}}}\\ 2x^{2}-3x\phantom{+6\phantom{00}}\\ \underline{2x^{2}-2x\phantom{+6\phantom{00}}}\\ -x+6\phantom{00}\\ \underline{-x+1\phantom{00}}\\ 5 \end{array}

よってあまり $5$

\begin{array}{r} x^{3}+x^{2}+4x+5\phantom{0000000000}\\ x-2{\overline{\big)\;x^{4}-x^{3}+2x^{2}-3x+6\phantom{00}}}\\ \underline{x^{4}-2x^{3}\phantom{+2x^{2}-3x+6\phantom{00}}}\\ x^{3}+2x^{2}\phantom{-3x+6\phantom{00}}\\ \underline{x^{3}-2x^{2}\phantom{-3x+6\phantom{00}}}\\ 4x^{2}-3x\phantom{+6\phantom{00}}\\ \underline{4x^{2}-8x\phantom{+6\phantom{00}}}\\ 5x+6\phantom{00}\\ \underline{5x-10\phantom{00}}\\ 16 \end{array}

よってあまり $16$

\begin{array}{r} x^{3}-4x^{2}+14x-45\phantom{0000000000}\\ x+3{\overline{\big)\;x^{4}-x^{3}+2x^{2}-3x+6\phantom{00}}}\\ \underline{x^{4}+3x^{3}\phantom{+2x^{2}-3x+6\phantom{00}}}\\ -4x^{3}+2x^{2}\phantom{-3x+6\phantom{00}}\\ \underline{-4x^{3}-12x^{2}\phantom{-3x+6\phantom{00}}}\\ 14x^{2}-3x\phantom{+6\phantom{00}}\\ \underline{14x^{2}+42x\phantom{+6\phantom{00}}}\\ -45x+6\phantom{00}\\ \underline{-45x-135\phantom{00}}\\ 141 \end{array}

よってあまり $141$

\begin{array}{r} x^2+2x+6 \\[-3pt] x^2-3x+2\overline{\big)\ x^4-x^3+2x^2-3x+6} \\ \underline{x^4-3x^3+2x^2\phantom{-3x+6}} \\ 2x^3\phantom{-6x^2+4x}-3x \\ \underline{2x^3-6x^2+4x} \\ 6x^2-7x+6 \\ \underline{6x^2-18x+12} \\ 11x-6 \end{array}

よってあまり $11x-6$