x³+x+2 x³+x²+x-3 分解因式
答案:2 悬赏:60
解决时间 2021-02-03 20:13
- 提问者网友：故事与他
- 2021-02-03 15:56
x³+x+2 x³+x²+x-3 分解因式
最佳答案
- 二级知识专家网友：萝莉姐姐鹿小北
- 2021-02-03 16:30
x³+x+2
=x³+2x²+x-2x²+2
=x(x²+2x+1)-2(x²-1)
=x(x+1)²-2(x+1)(x-1)
=(x+1)[x(x+1)-2(x-1)]
=(x+1)(x²+x-2x+2)
=(x+1)(x²-x+2)
x³+x²+x-3
=x³-2x²+x+3x²-3
=x(x²-2x+1)+3(x²-1)
=x(x-1)²+3(x+1)(x-1)
=(x-1)[x(x-1)+3(x+1)]
=(x-1)(x²-x+3x+3)
=(x-1)(x²+2x+3)
=x³+2x²+x-2x²+2
=x(x²+2x+1)-2(x²-1)
=x(x+1)²-2(x+1)(x-1)
=(x+1)[x(x+1)-2(x-1)]
=(x+1)(x²+x-2x+2)
=(x+1)(x²-x+2)
x³+x²+x-3
=x³-2x²+x+3x²-3
=x(x²-2x+1)+3(x²-1)
=x(x-1)²+3(x+1)(x-1)
=(x-1)[x(x-1)+3(x+1)]
=(x-1)(x²-x+3x+3)
=(x-1)(x²+2x+3)
全部回答
- 1楼网友：滚刀废物浮浪人
- 2021-02-03 17:49
(x-3)(x+2)-(x-7)=x²-x-6-x+7=x²-2x+1=(x-1)²。
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