Question

因式分解:X15+X14+X13+X12+X11+X10+X9+X8+X7+X6+X5+X4+X3+X2+X+1

X后面的数字表示它的指数,要过程,谢谢

Answer 1

X15+X14+X13+X12+X11+X10+X9+X8+X7+X6+X5+X4+X3+X2+X+1
=x^14(x+1)+x^12(x+1)+x^10(x+1)+x^8(x+1)+x^6(x+1)+x^4(x+1)+x^2(x+1)+(x+1)
=(x+1)(x^14+x^12+x^10+x^8+x^6+x^4+x^2+1)
.....
=(x+1)(x^2+1)(x^4+1)(x^8+1)

Answer 2

X15+X14+X13+X12+X11+X10+X9+X8+X7+X6+X5+X4+X3+X2+X+1
=（X15+X14）+（X13+X12）+（X11+X10）+（X9+X8）+（X7+X6）+（X5+X4）+(X3+X2)+(X+1)
=x14(x+1)+x12(x+1)+x10(x+1)+x8(x+1)+x6(x+1)+x4(x+1)+x2(x+1)+(x+1)
=(x+1)(x14+x12+x10+x8+x6+x4+x2+1)
=(x+1)[(x14+x12)+(x10+x8)+(x6+x4)+(x2+1)]
=(x+1)[x12(x²+1)+x8(x²+1)+x4(x²+1)+(x²+1)]
=(x+1)(x²+1)(x12+x8+x4+1)
=(x+1)(x²+1)[(x12+x8)+(x4+1)]
=(x+1)(x²+1)[x8(x4+1)+(x4+1)]
=(x+1)(x²+1)(x4+1)(x8+1)