Question

在有理数范围内因式分解x5＋x＋1

Answer 1

x^5 +x +1 = x^5 - x^2 + x^2 +x +1
= x^2 (x^3 -1 ) +(x^2 +x +1)
=x^2 (x-1)(x^2 +x +1) + (x^2 +x +1)
=(x^2 +x +1) (x^3 -x^2 +1 )