Question

分解因式：x的5次方+x的4次方+x的3 次方+x的平方+x+1

Answer 1

原式=x^4(x+1)+x²(x+1)+(x+1)
=(x+1)(x^4+x²+1)
=(x+1)(x^4+2x²+1-x²)
=(x+1)[(x²+1)²-x²]
=(x+1)(x²+x+1)(x²-x+1)

Answer 2

x^5+x^4+x^3+x^2+x+1=x^3(x^2+x+1)+(x^2+x+1) = (x^3+1)(x^2+x+1)
望采纳