高専の数学解説

第7章 7.8

x2+x−2=(x−1)(x+2)x^2+x-2=(x-1)(x+2)

x5+x4+x3+(a+1)x2+(a+1)x+(a+1)x−1) x6+ax3  b‾x6−x5‾x5x5−x4‾x4+ax3x4−x3‾(a+1)x3(a+1)x3−(a+1)x2‾(a+1)x2(a+1)x2−(a+1)x‾(a+1)x+b(a+1)x−(a+1)‾b+(a+1)\begin{array}{r} x^5+x^4+x^3+(a+1)x^2+(a+1)x+(a+1) \\[4pt] x-1\big)\ \overline{x^6 \qquad\qquad\qquad +ax^3 \qquad\qquad\qquad\qquad\qquad\ \ b} \\ \underline{x^6-x^5} \\ x^5 \\ \underline{x^5-x^4} \\ x^4+ax^3 \\ \underline{x^4-x^3} \\ (a+1)x^3 \\ \underline{(a+1)x^3-(a+1)x^2} \\ (a+1)x^2 \\ \underline{(a+1)x^2-(a+1)x} \\ (a+1)x+b \\ \underline{(a+1)x-(a+1)} \\ b+(a+1) \end{array} x5−2x4+4x3+(a−8)x2−2(a−8)x+4(a−8)x+2) x6+ax3  b‾x6+2x5‾−2x5−2x5−4x4‾4x4+ax34x4+8x3‾(a−8)x3(a−8)x3+2(a−8)x2‾−2(a−8)x2−2(a−8)x2−4(a−8)x‾4(a−8)x+b4(a−8)x+8(a−8)‾b−8(a−8)\begin{array}{r} x^5-2x^4+4x^3+(a-8)x^2-2(a-8)x+4(a-8) \\[4pt] x+2\big)\ \overline{x^6 \qquad\qquad\qquad +ax^3 \qquad\qquad\qquad\qquad\qquad\qquad\ \ b} \\ \underline{x^6+2x^5} \\ -2x^5 \\ \underline{-2x^5-4x^4} \\ 4x^4+ax^3 \\ \underline{4x^4+8x^3} \\ (a-8)x^3 \\ \underline{(a-8)x^3+2(a-8)x^2} \\ -2(a-8)x^2 \\ \underline{-2(a-8)x^2-4(a-8)x} \\ 4(a-8)x+b \\ \underline{4(a-8)x+8(a-8)} \\ b-8(a-8) \end{array}

b+a+1=0b+a+1=0

b−8a+64=0b-8a+64=0

これから a=7a=7 b=−8b=-8

解説: r31bn1z