求一道稍微难点的因式分解题
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/08/18 01:02:21
求一道稍微难点的因式分解题
用分组法的
用分组法的
![求一道稍微难点的因式分解题](/uploads/image/z/18781634-2-4.jpg?t=%E6%B1%82%E4%B8%80%E9%81%93%E7%A8%8D%E5%BE%AE%E9%9A%BE%E7%82%B9%E7%9A%84%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%E9%A2%98)
1
x^(n+5)+9x^(n+3)-162x^(n+1)
=x^(n+1)(x^4+9x²-162)
=x^(n+1)(x²+18)(x²-9)
=x^(n+1)(x²+18)(x+3)(x-3)
2.
(x²+5x+6)(x²+5x-2)+16
=(x²+5x+2+4)(x²+5x+2-4)+16
=(x²+5x+2)²-16+16
=(x²+5x+2)²
3.
2^n=(-2)^99+(-2)^100
=2^100-2^99
=2^99*(2-1)=2^99,
故n=99.
4.
(84a²b³c^4 d²)/(-96c²d³b^5 a )
=-(7ac²)/(8b²d)
(2xy-x²-y²+z²)/(2xz+x²-y²+z²)
=[z²-(x-y)²]/[(x+z)²-y²]
=[(x-y+z)(-x+y+z)]/[(x-y+z)(x+y+z)]
=(y+z-x)/(x+y+z)
5.
[-a²+a²/(a-1)-a-1]*(a³-1)/(a²+a+1)
=a²*(a³-1)/[(a²+a+1)(a-1)]+(-a²-a-1)*(a³-1)/(a²+a+1)
=a²-(a³-1)
= -a³+a²+1
x^(n+5)+9x^(n+3)-162x^(n+1)
=x^(n+1)(x^4+9x²-162)
=x^(n+1)(x²+18)(x²-9)
=x^(n+1)(x²+18)(x+3)(x-3)
2.
(x²+5x+6)(x²+5x-2)+16
=(x²+5x+2+4)(x²+5x+2-4)+16
=(x²+5x+2)²-16+16
=(x²+5x+2)²
3.
2^n=(-2)^99+(-2)^100
=2^100-2^99
=2^99*(2-1)=2^99,
故n=99.
4.
(84a²b³c^4 d²)/(-96c²d³b^5 a )
=-(7ac²)/(8b²d)
(2xy-x²-y²+z²)/(2xz+x²-y²+z²)
=[z²-(x-y)²]/[(x+z)²-y²]
=[(x-y+z)(-x+y+z)]/[(x-y+z)(x+y+z)]
=(y+z-x)/(x+y+z)
5.
[-a²+a²/(a-1)-a-1]*(a³-1)/(a²+a+1)
=a²*(a³-1)/[(a²+a+1)(a-1)]+(-a²-a-1)*(a³-1)/(a²+a+1)
=a²-(a³-1)
= -a³+a²+1