x^3+x-30(分解因式);x^12-y^12;x^15+x^14+x^13....x^2+x+1

x^3+x-30(分解因式)

=(x^3-27)+(x-3)
=(x-3)(x^2+3x+9)+(x-3)
=(x-3)(x^2+3x+9+1)
=(x-3)(x^2+3x+10)

;x^12-y^12;

=(x^6+y^6)(x^6-y^6)
=(x^2+y^2)(x^4-x^2y^2+y^4)(x^3+y^3)(x^3-y^3)
=(x^2+y^2)(x^4-x^2y^2+y^4)(x+y)(x^2-xy+y^2)(x-y)(x^2+xy+y^2)

x^15+x^14+x^13....x^2+x+1

=x^14(x+1)+x^13(x+1)+...+x^2+(x+1)

=(x+1)(x^14+x^13+...+x^2+1)

x^3+x-30=(x+6)(x-5)
x^12-y^12
=(x+y)(x-y)
x^15+x^14+x^13....x^2+x+1
=(x+1)(x^14+x^12....z^2+1)