在实数范围内分解因式(x²-1)(x²+2)-40=

来源：学生作业学帮网编辑：学帮网时间：2024/07/10 20:23:20

令t=x^2
(x^2-1)(x^2+2)-40
=(t-1)(t+2)-40
=t^2+t-42
=(t^2-6t)+(7t-42)
=t(t-6)+7(t-6)
=(t+7)(t-6)
=(x^2+7)(x^2-6)
=(x^2+7)(x+√6)(x-√6)

(x²-1)(x²+2)-40=(x²-1)(x²+1)+x²-1-40=x^4-1+x²-1-40=x^4+x²-42=(x²-7)(x²+6)=(x-√7)(x+√7)(x²+6)