Question

因式分解 x^8+x^7+x^6+x^5+x^4+x^3+x^2+x=?

Answer 1

原式=x^5(x^3+x^2+x+1)+x(x^3+x^2+x+1)

=x(x^4+1)(x^3+x^2+x+1)

=x(x^4+1)[x^2(x+1)+(x+1)]

=x(x^4+1)(x^2+1)(x+1)