Question

因式分解，求详细过程

Answer 1

2x³-6x²-6x+2
=2x³+2x²-8x²-8x+2x+2
=2x²(x+1)-8x(x+1)+2(x+1)
=(2x²-8x+2)(x+1)
=2(x²-4x+1)(x+1)
如果是在实数范围内因式分解，还可以继续分解：
=2(x²-4x+4-3)(x+1)
=2[(x-2)²-3](x+1)
=2(x-2+√3)(x-2-√3)(x+1)

还可以这样分解：
2x³-6x²-6x+2
=(2x³+2)-(6x²+6x)
=2(x³+1)-6x(x+1)
=2(x+1)(x²-x+1)-6x(x+1)
=2(x+1)(x²-x+1-3x)
=2(x+1)(x²-4x+1)
后面的和上面第一种解法一样。

Answer 2

2x³-6x²-6x+2
=2(x³-3x²-3x+1)
=2(x³+x²-4x²-3x+1)
=2[x²(x+1)-(4x²+3x-1)]
=2[(x+1)x²-(x+1)(4x-1)]
=2(x+1)(x²-4x+1)
=2(x+1)(x-2-√5)(x-2+√5)

Answer 3

2(x³+1)-6x(x+1)=2(x+1)(x²+1-x)-6x(x+1)=2(x+1)(x²+1-4x)