因式分解x3-x2-x=1 x3+x2-x-1怎么因式分解？
x3+x+2 \u600e\u4e48\u56e0\u5f0f\u5206\u89e3 \u8be6\u7ec6\u8fc7\u7a0b\u8c22\u8c22x³+x+2
=(x³+1)+(x+1)
=(x+1)(x²-x+1)+(x+1)
=(x+1)(x²-x+1+1)
=(x+1)(x²-x+2)
x"\u2019 + x\u201d - x - 1
= x\u201d( x + 1 ) - ( x + 1 )
= ( x + 1 )( x" - 1 )
= ( x + 1 )( x + 1 )( x - 1 )
= ( x + 1 )\u201d( x - 1 )
\u6216\u8005
= x"\u2019 - x + x\u201d - 1
= x( x" - 1 ) + ( x" - 1 )
= ( x + 1 )( x" - 1 )
= ( x + 1 )( x + 1 )( x - 1 )
= ( x + 1 )"( x - 1 )
\u6216\u8005
= x"\u2019 - 1 + x\u201d - x
= ( x - 1 )( x\u201d + x + 1 ) + x( x - 1 )
= ( x - 1 )( x\u201d + x + 1 + x )
= ( x" + 2x + 1 )( x - 1 )
= ( x + 1 )"( x - 1 )
x3-x2-x+1 = x^3 - x -(x^2 -1) = x(x^2 - 1) - (x^2 - 1) = (x - 1)(x^2 - 1) = (x-1)(x-1)(x+1)=(x+1)(x-1)^2
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绛旓細涓嶇敤瑙ｄ竴鍏冧簩娆℃柟绋嬬粍 浣犱竴瀹氬垰瀛鍥犲紡鍒嗚В鍚 鐢眡^2-x-1=0寰梮^2=x+1 x^2-x=1 鏁厁^3-2x=x(x^2-2)=x锛坸+1-2锛=x锛坸-1锛=x^2-x=1 浠涔堟眰鍊煎晩 浣犱笉鏄浜唜^3-2x=1鍚楋紵 姹倄锛熼偅灏辩敤姹傛牴鍏紡 瑙ｅ緱x=锛1卤鈭5锛/2 ...
绛旓細x^3 - 1 杩涜鍥犲紡鍒嗚В锛屽緱鍒 (x-1)(x^2+x+1)銆傚洜姝わ紝鍘熷琛ㄨ揪寮忓彲浠ュ啓鎴愶細x(x-1) / [(x-1)(x^2+x+1)]鎺ヤ笅鏉ワ紝鎴戜滑鍙互灏嗗垎瀛愬拰鍒嗘瘝涓浉鍚岀殑鍥犲紡 x-1 绾︽帀锛屽緱鍒版渶绠褰㈠紡锛歺 / (x^2 + x + 1)鍥犳锛寈^2 - x / (x^3 - 1) 鍖栫畝鍚庝负 x / (x^2 + x + 1)銆
绛旓細鍥犲紡鍒嗚В 瑙ｏ細X3-x2-x-2=x^3-8-(x^2+x-6)=(x-2)(x^2+2x+4)-(x-2)(x+3)=(x-2)(x^2-x+1)=0 鍒檟-2=0鎴杧^2-x+1=0 瑙ｅ緱x=2
绛旓細x^3-2x+1 =x^3-x^2+(x^2-2x+1)=x^2(x-1)+(x-1)^2 =(x-1)(x^2+x-1)
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