因式分解:x^4+2x^3-9x^2-2x+8
答案:6 悬赏:70 手机版
解决时间 2021-11-14 15:42
- 提问者网友：缘字诀
- 2021-11-14 01:43
因式分解:x^4+2x^3-9x^2-2x+8
最佳答案
- 五星知识达人网友：十年萤火照君眠
- 2021-11-14 02:21
=x^4+x³+x³+x²-10x²-10x+8x+8
=x³(x+1)+x²(x+1)-10x(x+1)+8(x+1)
=(x+1)(x³+x²-10x+8)
=(x+1)(x³-x²+2x²-2x-8x+8)
=(x+1)(x-1)(x²+2x-8)
=(x+1)(x-1)(x+4)(x-2)
=x³(x+1)+x²(x+1)-10x(x+1)+8(x+1)
=(x+1)(x³+x²-10x+8)
=(x+1)(x³-x²+2x²-2x-8x+8)
=(x+1)(x-1)(x²+2x-8)
=(x+1)(x-1)(x+4)(x-2)
全部回答
- 1楼网友：荒野風
- 2021-11-14 06:30
=x^4+x³+x³+x²-10x²-10x+8x+8
=x³(x+1)+x²(x+1)-10x(x+1)+8(x+1)
=(x+1)(x³-x²+2x²-2x-8x+8)
=(x+1)(x-1)(x²+2x-8)
=(x+1)(x-1)(x+4)(x-2)
=x³(x+1)+x²(x+1)-10x(x+1)+8(x+1)
=(x+1)(x³-x²+2x²-2x-8x+8)
=(x+1)(x-1)(x²+2x-8)
=(x+1)(x-1)(x+4)(x-2)
- 2楼网友：英雄的欲望
- 2021-11-14 05:36
=x^4 - x^3 + 3x^3 - 3x^2 - 6x^2 + 6x - 8x + 8
=(x-1)(x^3 +3x^2 - 6x - 8)
= (x-1)(x^3 + x^2 + 2x^2 + 2x - 8x - 8)
= (x-1)(x+1)(x^2 + 2x - 8)
= (x-1)(x+1)(x+4)(x-2)
=(x-1)(x^3 +3x^2 - 6x - 8)
= (x-1)(x^3 + x^2 + 2x^2 + 2x - 8x - 8)
= (x-1)(x+1)(x^2 + 2x - 8)
= (x-1)(x+1)(x+4)(x-2)
- 3楼网友：撞了怀
- 2021-11-14 05:13
x^4+2x³-9x²-2x+8
=x^4-2x³+4x³-8x²-x²+2x-4x+8
=x³(x-2)+4x²(x-2)-x(x-2)-4(x-2)
=(x-2)(x³+4x²-x-4)
=(x-2)[x²(x+4)-(x+4)]
=(x-2)(x+4)(x²-1)
=(x-2)(x+4)(x+1)(x-1)
=x^4-2x³+4x³-8x²-x²+2x-4x+8
=x³(x-2)+4x²(x-2)-x(x-2)-4(x-2)
=(x-2)(x³+4x²-x-4)
=(x-2)[x²(x+4)-(x+4)]
=(x-2)(x+4)(x²-1)
=(x-2)(x+4)(x+1)(x-1)
- 4楼网友：神的生死簿
- 2021-11-14 03:41
(x+1)(x-1)(x-2)(x+4)
- 5楼网友：酒醒三更
- 2021-11-14 03:05
x^4+2x^3-9x^2-2x+8
=x^4-2x^3+4x^3-8x^2-x^2+2x-4x+8
=(x^3+4x^2-x-4)(x-2)
=[x(x+1)(x-1)+4(x+1)(x-1)](x-2)
=(x+1)(x-1)(x-2)(x+4)
=x^4-2x^3+4x^3-8x^2-x^2+2x-4x+8
=(x^3+4x^2-x-4)(x-2)
=[x(x+1)(x-1)+4(x+1)(x-1)](x-2)
=(x+1)(x-1)(x-2)(x+4)
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