X^4+2x^3-3x^2-4x+4,因式分解
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X^4+2x^3-3x^2-4x+4,因式分解
![](http://img.wesiedu.com/upload/7/c6/7c6b0984a54c47b50e26c17508177f06.jpg)
![](http://img.wesiedu.com/upload/7/c6/7c6b0984a54c47b50e26c17508177f06.jpg)
![X^4+2x^3-3x^2-4x+4,因式分解](/uploads/image/z/2351888-8-8.jpg?t=X%5E4%2B2x%5E3-3x%5E2-4x%2B4%2C%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3)
x4次方+2x³-3x²-4x+4
=x²﹙x²+2x-3﹚-﹙4x-4﹚
=x²﹙x+3﹚﹙x-1﹚-4﹙x-1﹚
=﹙x-1﹚[x²﹙x+3﹚-4]
=﹙x-1﹚﹙x³+3x²-4﹚
=﹙x-1﹚[﹙x³-1﹚+﹙3x²-3﹚]
=﹙x-1﹚[﹙x-1﹚﹙x²+x+1﹚+3﹙x²-1﹚]
=﹙x-1﹚[﹙x-1﹚﹙x²+x+1﹚+3﹙x+1﹚﹙x-1﹚]
=﹙x-1﹚﹙x-1﹚[﹙x²+x+1﹚+3﹙x+1﹚]
=﹙x-1﹚²﹙x²+x+1+3x+3﹚
=﹙x-1﹚²﹙x²+4x+4﹚
=﹙x-1﹚²﹙x+2﹚²
再问:![](http://img.wesiedu.com/upload/f/88/f88100150469d8e93235169ce6df25c2.jpg)
再问: 第二题我不会,请你告诉我谢谢
再答: 3x³-5x²y+xy²+y³
=3x³-3x²y+﹙-2x²y+xy²+y³﹚
=3x²﹙x-y﹚-y﹙2x²-xy-y²﹚
=3x²﹙x-y﹚-y﹙2x+y﹚﹙x-y﹚
=﹙x-y﹚[3x²-y﹙2x+y﹚]
=﹙x-y﹚﹙3x²-2xy-y²﹚
=﹙x-y﹚﹙3x+y﹚﹙x-y﹚
=﹙x-y﹚²﹙3x+y﹚
=x²﹙x²+2x-3﹚-﹙4x-4﹚
=x²﹙x+3﹚﹙x-1﹚-4﹙x-1﹚
=﹙x-1﹚[x²﹙x+3﹚-4]
=﹙x-1﹚﹙x³+3x²-4﹚
=﹙x-1﹚[﹙x³-1﹚+﹙3x²-3﹚]
=﹙x-1﹚[﹙x-1﹚﹙x²+x+1﹚+3﹙x²-1﹚]
=﹙x-1﹚[﹙x-1﹚﹙x²+x+1﹚+3﹙x+1﹚﹙x-1﹚]
=﹙x-1﹚﹙x-1﹚[﹙x²+x+1﹚+3﹙x+1﹚]
=﹙x-1﹚²﹙x²+x+1+3x+3﹚
=﹙x-1﹚²﹙x²+4x+4﹚
=﹙x-1﹚²﹙x+2﹚²
再问:
![](http://img.wesiedu.com/upload/f/88/f88100150469d8e93235169ce6df25c2.jpg)
再问: 第二题我不会,请你告诉我谢谢
再答: 3x³-5x²y+xy²+y³
=3x³-3x²y+﹙-2x²y+xy²+y³﹚
=3x²﹙x-y﹚-y﹙2x²-xy-y²﹚
=3x²﹙x-y﹚-y﹙2x+y﹚﹙x-y﹚
=﹙x-y﹚[3x²-y﹙2x+y﹚]
=﹙x-y﹚﹙3x²-2xy-y²﹚
=﹙x-y﹚﹙3x+y﹚﹙x-y﹚
=﹙x-y﹚²﹙3x+y﹚