Question

因式分解：X的4次方+X的3次方-3X的平方-4X-4

在线等，速度的给分！！！！！

Answer 1

先把因式拆成能提公因式并有公因式的形式：
x^4+x^3-3x^2-4x-4
=x^4+x^3+x^2-4x^2-4x-4
=x^2(x^2+x+1)-4(x^2+x+1)
=(x^2+x+1)(x^2-4)
=(x^2+x+1)(x+2)(x-2)
最后看看有没有分解彻底，发现x^2-4还能分解

因此答案为x^2+x+1)(x+2)(x-2)

Answer 2

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

Answer 3

x^4+x^3-3x^2-4x-4
=(x^4+2x^3)-(x^3+2x^2)-(x^2+2x)-(2x+4)
=(x^3)(x+2)-(x^2)(x+2)-x(x+2)-2(x+2）
=（x^3-x^2-x-2)(x+2)
=[(x^3-2x^2)+(x^2-2x)+(x-2)](x+2)
=(x-2)(x+2)(x^2+x+1)
1楼正解

Answer 4

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

Answer 5

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