第1章 1.32 | 高専の数学解説

(1)

\begin{array}{r} 3x^2-x+4 \\ \hline 2x^2+x-1)\ 6x^4+x^3+4x^2+5x-4 \\ \underline{6x^4+3x^3-3x^2\phantom{+5x-4}} \\ -2x^3+7x^2+5x\phantom{-4} \\ \underline{-2x^3-x^2+x\phantom{-4}} \\ 8x^2+4x-4 \\ \underline{8x^2+4x-4} \\ 0 \end{array}

\begin{array}{r} 2a^2+2a+1 \\ \hline a^2-a+1)\ 2a^4+a^2+2 \\ \underline{2a^4-2a^3+2a^2\phantom{+2}} \\ 2a^3-a^2\phantom{+2} \\ \underline{2a^3-2a^2+2a\phantom{}} \\ a^2-2a+2 \\ \underline{a^2-a+1} \\ -a+1 \end{array}

\begin{array}{r} 2x^2+5x-1 \\ \hline x^2-2x+4)\ 2x^4+x^3-3x^2+20x \\ \underline{2x^4-4x^3+8x^2\phantom{+20x}} \\ 5x^3-11x^2+20x \\ \underline{5x^3-10x^2+20x} \\ -x^2 \\ \underline{-x^2+2x-4} \\ -2x+4 \end{array}

\begin{array}{r} x+2y+3 \\ \hline x+3y+5)\ x^2+5xy+6y^2+8x+19y+15 \\ \underline{x^2+3xy+5x\phantom{+6y^2+19y+15}} \\ 2xy+6y^2+3x+19y \\ \underline{2xy+6y^2+10y\phantom{+3x}} \\ 3x+9y+15 \\ \underline{3x+9y+15} \\ 0 \end{array}