1.X的5次方+1 2.X的7次方+1的因式分解

Question

..弄错是X的7次方-1

Answer 1

题目:x^5+1和x^7-1

分析:这两道题目是查考学生的思维创新能力,可以巧妙地增加一些式子以达到因式分解的目的

思路:增加一些式子并减少它,将他们分配成组,两次提取公因式即可

解:x^5+1
=x^5+x^4-x^4-x^3+x^3+x^2-x^2-x+x+1
=x^4(x+1)-x^3(x+1)+x^2(x+1)-x(x+1)+(x+1)
=(x+1)(x^4-x^3+x^2-x+1)

x^7-1
=x^7-x^6+x^6-x^5+x^5-x^4+x^4-x^3+x^3-x^2+x^2-x+x-1
=x^6(x-1)+x^5(x-1)+x^4(x-1)+x^3(x-1)+x^2(x-1)+x(x-1)+(x-1)
=(x-1)(x^6+x^5+x^4+x^3+x^2+x+1)

Answer 2

在原式上加减一些式子,提取公因式

x5+1
=x5+x4-x4-x3+x3+x2-x2-x+x+1
=x4(x+1)-x3(x+1)+x2(x+1)-x(x+1)+(x+1)
=(x+1)(x4-x3+x2-x+1)

x7-1
=x7-x6+x6-x5+x5-x4+x4-x3+x3-x2+x2-x+x-1
=x6(x-1)+x5(x-1)+x4(x-1)+x3(x-1)+x2(x-1)+x(x-1)+(x-1)
=(x-1)(x6+x5+x4+x3+x2+x+1)

Answer 3

这是x^3+1与x^3-1的推论 如果是x^n+1与x^n-1k更据规律同样得出
要用好地方法啊 不要只解题 要动脑子

参考资料：大脑

Answer 4

x^5+1
=x^5+x^4-x^4-x^3+x^3+x^2-x^2-x+x+1
=x^4(x+1)-x^3(x+1)+x^2(x+1)-x(x+1)+(x+1)
=(x+1)(x^4-x^3+x^2-x+1)

x^7-1
=x^7-x^6+x^6-x^5+x^5-x^4+x^4-x^3+x^3-x^2+x^2-x+x-1
=x^6(x-1)+x^5(x-1)+x^4(x-1)+x^3(x-1)+x^2(x-1)+x(x-1)+(x-1)
=(x-1)(x^6+x^5+x^4+x^3+x^2+x+1)本回答被提问者采纳