Question

因式分解，要过程

Answer 1

5.
x(x+2)²(x+4)+4
=(x+2)²(x²+4x)+4
=(x+2)²[(x+2)²-4]+4
=(x+2)⁴-4(x+2)²+4
=[(x+2)²-2]²
=(x²+4x+2)²
6.
(x²-1)(x²+6x+8)+9
=(x²-1)[(x+3)²-1]+9
=x²(x+3)²-x²-(x+3)²+9
=x²(x+3)²-(2x²+6x)
=x²(x+3)²-2x(x+3)
=x(x+3)[x(x+3)-2]
=x(x+3)(x²+3x-2)
7.
x^(n+1) -3xⁿ+2x^(n-1)
=x^(n-1) (x²-3x+2)
=x^(n-1) (x-1)(x-2)
8.
x⁴+x²-6
=(x²+3)(x²-2) 如果是实数范围内分解的话，还可以继续，否则到这步就可以了
=(x²+3)(x+√2)(x-√2) 如果是实数范围内分解的话到这步就可以了，如果是复数范围，继续
=(x+√3i)(x-√3i)(x+√2)(x-√2) 这是包括复数范围的分解结果
9.
x^6-y^6
=(x³-y³)(x³+y³)
=(x-y)(x²+xy+y²)(x+y)(x²-xy+y²)
10.
x^5 -x³+x²-1
=x³(x²-1)+(x²-1)
=(x²-1)(x³+1)
=(x+1)(x-1)(x+1)(x²-x+1)
=(x+1)²(x-1)(x²-x+1)

以后出题，最好写明在什么范围内分解。

Answer 2

解：x(x+2)²(x+4)+4 (x²-1)(x²+6x+8)+9
=[x(x+4)](x+2)²+4 =(x+1)(x-1)(x+2)(x+4)+9
=[(x+2)²-4](x+2)²+4 =[(x+1)(x+2)][(x-1)(x+4)]+9
=(x+2)⁴-4(x+2)²+4 =(x²+3x+2)(x²+3x-4)+9
=[(x+2)²-2]² =(x²+3x)²-2(x²+3x)+1
=[(x+2+√2)(x+2-√2)]² =(x²+3x-1)²=[(x+3/2+√13/2)(x+3/2-√13/2)]²
x^(n+1)-3x^n+2x^(n-1)=(x²-3x+2)x^(n-1)=(x-1)(x-2)x^(n-1)
x⁴+x²-6=(x²+3)(x²-2)=(x²+3)(x+√2)(x-√2)
x^6-y^6=(x³+y³)(x³-y³)=(x+y)(x²-xy+y²)(x-y)(x²+xy+y²)
x^5-x³+x²-1=(x^5-x³)+(x²-1)=x³(x²-1)+(x²-1)=(x³+1)(x²-1)=(x²-x+1)(x+1)²(x-1)

追问

谢谢