Math III Section 4.6 problem #29
"Frank says: that since there is only one sign change in P(-x), that there must only be one negative real root."
So with the knowledge i gathered with the work above Frank is wrong because instead of 1 negative real root there are 1,3 negative real roots.
P(-x)=-x^3-x^2-x+1. When it should have been P(-x)=-x^3+x^2-x+1.