x^15+x^12+x^9+x^6+x^3+1因式分解数学题

把x^3看成m，则原式=m^5+m^4+m^3+m^2+m^1+m^0,有等比数列的求和公式可得
m*(1-m^6)/(1-m),，再把m以替换为x^3就行了

x^15+x^12+x^9+x^6+x^3+1
=x^9*（x^6+x^3+1）+（x^6+x^3+1）
=（x^6+x^3+1）*（x^9+1）
=（x^6+x^3+1）*（x^3+1）*（x^6-x^3+1）
=（x^6+x^3+1）*（x+1）*（x^2-x+1）*（x^6-x^3+1）

答：
x^15+x^12+x^9+x^6+x^3+1
=(x^3+1)x^12+(x^3+1)x^6+(x^3+1)
=(x^3+1)(x^12+x^6+1)
=(x+1)(x^2-x+1)(x^12+2x^6+1-x^6)
=(x+1)(x^2-x+1)[(x^6+1)^2-x^6]
=(x+1)(x^2-x+1)(x^6-x^3+1)(x^6+x^3+1)

x^15+x^12+x^9+x^6+x^3+1
=x^12(x^3+1)+x^6(x^3+1)+(x^3+1）
=(x^3+1)（x^12+x^6+1)

原式=x^12(x³+1)+x^6(x³+1)+（x³+1）
=(x³+1)(x^12+x^6+1)
=(x+1)(x²-x+1)(x^12+x^6+1)
=(x+1)(x²-x+1)(x^12+2x^6+1-x^6)
=(x+1)(x²-x+1)[(x^6+1)²-x^6]
=(x+1)(x²-x+1)(x^6+x³+1)(x^6-x³+1)
请点击下面的【选为满意回答】按钮,

原式=x12（x3+1)+x6(x3+1)+x3+1
=(x12+x6+1)(x3+1)

原式=x^12(x³+1)+x^6(x³+1)+(x³+1)
=(x³+1)(x^12+x^6+1)
=(x+1)(x²-x+1)(x^12+2x^6+1-x^6)
=(x+1)(x²-x+1)[(x^6+1)²-x^6]
=(x+1)(x²-x+1)(x^6+x³+1)(x^6-x³+1)