因式分解:x 4+3x 3-4x 2-8x

2020-11-26 18:37:30 字数 3802 阅读 9353

1楼:匿名用户

解:x+3x-4x-8x+8

=x+x-2x+2x+2x-4x-4x-4x+8=x(x+x-2)+2x(x+x-2)-4(x+x-2)=(x+x-2)(x+2x-4)

=(x-1)(x+2)(x+2x+1-5)=(x-1)(x+2)[(x+1)-5]=(x-1)(x+2)(x+1+√5)(x+1-√5)

2楼:蓝精灵

=x^2(x^2+3x-4)-8x+8

=x^2(x+4)(x-1)-8(x-1)

=(x-1)(x^3+4x^2-8)

因式分解x^4-4x^3+3x^2+4x-4

3楼:数学爱好者

x^2=1代入原式=1-4x+3+4x-4=0∴原式含有(x^2-1)这个因式

原式=x^4-x^2-(4x^3-4x)+4x^2-4=(x^2-1)(x^2-4x+4)

=(x-1)(x+1)(x-2)^2

解法2原式=x^4+3x^2-4-(4x^3-4x)=(x^2-1)(x^2+4)-4x(x^2-1)=(x^2-1)(x^2+4-4x)

=(x-1)(x+1)(x-2)^2

因式分解:x^4+2x^3-9x^2-2x+8

4楼:匿名用户

=x^4+x+x+x-10x-10x+8x+8=x(x+1)+x(x+1)-10x(x+1)+8(x+1)=(x+1)(x+x-10x+8)

=(x+1)(x-x+2x-2x-8x+8)=(x+1)(x-1)(x+2x-8)

=(x+1)(x-1)(x+4)(x-2)

5楼:反**也反皇帝

^^^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)

6楼:樱之落痕

(x+1)(x-1)(x-2)(x+4)

因式分解:x^4-3x^3-2x^2+12x-8

7楼:匿名用户

解:令代数式=0

可知当x=1时,上式为零,所以(x-1)必为上式的因式之一x^4-3x^3-2x^2+12x-8

=x^3(x-1)-2x^2(x-1)-4x(x-1)+8(x-1)=(x^3-2x^2-4x+8)(x-1)=(x-1)

=(x^2-4)(x-2)(x-1)

=(x+2)(x-1)(x-2)^2

8楼:匿名用户

x*4-3x*3+2x*2-4x*2+12x-8x*2(x*2-3x+2)-4x*2+12x-8x*2(x-2)(x-1)+(4x*2-12x+8)x*2(x-2)(x-1)+(x-1)(4x-8)(x-1)(x*2(x-2)+(4x-8))(x-1)(x*2(x-2)+4(x-2))(x-1)(x-2)(x*2)(x*2+4)

x^4-4x^3+8x^2-8x-12因式分解

9楼:匿名用户

设 x^4-4x+8x-8x-12=(x+ax+b)(x+cx+d)

=x^4+(a+c)x+(b+ac+d)x+(bc+ad)x+bd

故a+c=-4.........①;b+ac+d=8.......②

bc+ad=-8........③;bd=-12..............④

联立求解得:a=-2;c=-2;b=6;d=-2.

∴x^4-4x+8x-8x-12=(x-2x+6)(x-2x-2)

因式分解:x^4+2x^3-3x^2-4x+4

10楼:尹六六老师

=(x^2+x)^2-4(x^2+x)+4

=(x^2+x-2)^2

=(x-1)^2·(x+2)^2

11楼:

=(x^4+2x^3-3x^2)-(4x-4)=x(x+2x-3)-4(x-1)

=x(x+3)(

x-1)-4(x-1)

=(x-1)(x+3x)-4(x-1)=(x-1)(x+3x-4)

=(x-1)(x+2x+x+2x-2x-4)=(x-1)【x(x+2)+x(x+2)-2(x+2)】=(x-1)(x+2)(x+x-2)

=(x-1)(x+2)(x+2)(x-1)=(x-1)(x+2)

因式分解:x^4+2x^3-9x^2-2x+8

12楼:文仙灵儿

^^^x^4+2x^3-9x^2-2x+8

=x^4+2x^3-8x^2-x^2-2x+8=x^2*(x^2+2x-8)-(x^2+2x-8)=(x^2-1)(x^2+2x-8)

=(x+1)(x-1)(x-2)(x+4)

13楼:匿名用户

=x^3(x-2)+4x^2(x-2)-x(x-2)-4(x-2)=(x-2)(x^3+4x^2-x-4)=(x-2)(x^3-x^2+5x^2-5x+4x-4)

=(x-2)[x^2(x-1)+5x(x-1)+4(x-1)]=(x-2)(x-1)(x^2+5x+4)=(x-2)(x-1)(x+1)(x+4)

因式分解x^4-4x^3+4x^2-1

14楼:匿名用户

=(x^2-2x)^2-1

=(x^2-2x-1)(x^2-2x+1)=(x^2-2x-1)(x-1)^2

=(x-1+√2)(x-1-√2)(x-1)^2

15楼:匿名用户

^^^x^4-4x^3+4x^2-1

=x^4-x^3-3x^3+3x^2+x^2-1=x^3(x-1)-3x^2(x-1)+(x+1)(x-1)=(x-1)(x^3-3x^2+x+1)

=(x-1)[x^3-x^2-2x^2+2x-x+1]=(x-1)[x^2(x-1)-2x(x-1)-(x-1)]=(x-1)^2(x^2-2x-1)

=(x-1)^2(x^2-2x+1-2)

=(x-1)^2[(x-1)^2-2]

=(x-1)^2(x-1+√2)(x-1-√2)

16楼:匿名用户

x^8-8x^8y^8-8y^8 =(x^8)^8-8×8x^8y^8-(8y)^8 =(x^8-8y)^8

17楼:兆健郗芳林

(x^2-x-1)(x^2-3x-1)

因式分解 x^4+3x^3+6x^2-4怎么解?急!!!

18楼:匿名用户

^^x^4+3x^3+6x^2-4

=x^4+3x^3+2x^2+4x-4

=x(x+3x+2)+4(x-1)

=x(x+2)(x+1)+4(x+1)(x-1)=(x+1)(x+2x+4x-4)

19楼:匿名用户

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