Question

求x^3-3x^2-9x-5=0;因式分解的过程

Answer 1

x^3-3x^2-9x-5
=x^3+x^2-4x^2-4x-5x-5
=x^2(x+1)-4x(x+1)-5(x+1)
=(x+1)(x^2-4x-5)
=(x+1)(x+1)(x-5)
=[(x+1)^2](x-5)
=0
因此(x+1)^2=0,或x-5=0
解为：x=-1,x=5