题目

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

提问时间：2020-12-14

答案

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)