分解因式X5+X4+X3+X2+X+1X5为X的平方
问题描述：
分解因式X5+X4+X3+X2+X+1
X5为X的平方
答
(X5+X4+X3+X2+X+1)(X-1)
=x6-1
=(X3+1)(X3-1)
=(X+1)(X-1)(X2+X+1)(X2-X+1)
所以X5+X4+X3+X2+X+1
=(X+1)(X2+X+1)(X2-X+1)
答
原式=x^4(x+1)+x^2(x+1)+(x+1)
=(x+1)[(x^4+2x^2+1)-x^2]
=(x+1)[(x^2+1)^2-x^2]
=(x+1)(x^2+x+1)(x^2-x+1)