Question

x^4-10x^3+35x^2-50x-96如何分解因式

Answer 1

经试根,x=6和x=-1时,原式=0

所以有因式x-6和x+1

x^4-10x^3+35x^2-50x-96

=x^4-6x^3-4x^3+24x^2+11x^2-50x-96

=x^3(x-6)-4x^2(x-6)+(11x+16)(x-6)

=(x-6)(x^3-4x^2+11x+16)

=(x-6)(x^3+x^2-5x^2+11x+16)

=(x-6)[x^2(x+1)-(5x-16)(x+1)]

=(x-6)(x+1)(x^2-5x+16)