已知多項式x^4-x^3+mx^2+x-1,能被x-1整除,求m值

已知多項式x^4-x^3+mx^2+x-1,能被x-1整除,求m值

x^4-x^3+mx^2+x-1
=x^3(x-1)+(x-1)+mx^2
=(x^3+1)(x-1)+mx^2
能被x-1整除,即X不論取何值,都能被整除.顯然,m=0時,多項式=(x^3+1)(x-1)滿足條件.