factorize please

Question

-x³+4x²-23x+20=0

Answer 1

If there is a rational solution, it will be a factor of 20.  ±1,±2,±4,±5±10.

Try for f(x)=-x³+4x²-23x+20=0.  f(1)=-1=4-23=20=0.  (x-1) is a factor of f(x)

Divide, and get f(x)=(x-1)(-x²+3x-20).  The discriminant of the quadratic is negative.  There are no more real roots.  If you solve the quadratic -x²+3x-20=0, the roots are

x=[-3±√(9-4(-1)(-20))]/-2 =[3±i√71]/2 and so you can factor further as the product of

-(x-1)(x-[3-i√71]/2)(x-[3+i√71]/2).   Sorry for  the prior error!