因式分解x^15+x^14+x^13+…+x^2+x+1

2024-12-23 01:39:43

推荐回答（2个）

回答1：

x^15+x^14+x^13+…+x^2+x+1
=x^14(x+1)+x^12(x+1)+x^10(x+1)+...........+x^2(x+1)+(x+1)
=(x+1)(x^14+x^12+x^10+....+x^2+1)
=(x+1)(x^2+1)(x^12+x^8+x^4+1)
=(x+1)(x^2+1)(x^4+1)(x^8+1)

回答2：

x^15+X^14+X^13+……+x^2+X+1=(x^15+X^14)+(x^13+x^12)+(x^11+x^10)+.....+(x+1)
=x^14(x+1)+x^12(x+1)+x^10(x+1)+....+(x+1)
=(x+1)(x^14+x^12+x^10+...+x^2+1)
=(x+1)[x^12(x^2+1)+x^8(x^2+1)+x^4(x^2+1)+(x^2+1)]
=(x+1)(x^2+1)(x^12+x^8+x^4+1)
=(x+1)(x^2+1)[x^8(x^4+1)+(x^4+1)]
=(x+1)(x^2+1)(x^4+1)(x^8+1)