Question

已知多项式x^4-x^3+mx^2+x-1,能被x-1整除,求m值

Answer 1

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不论取何值,都能被整除.显然,m=0时,多项式=(x^3+1)(x-1)满足条件.