cleared_factorization= 2*(t + 1)**2*(t**4 - 4*t**3 - 2*t**2 - 12*t + 1)
expanded= 2*t**6 - 4*t**5 - 18*t**4 - 40*t**3 - 50*t**2 - 20*t + 2
at_t_5= 1152
derivative= 4*(t + 1)*(3*t**4 - 8*t**3 - 10*t**2 - 20*t - 5)
shifted_coefficients= [2, 56, 632, 3600, 10400, 12480, 1152]
OK: cleared polynomial has strictly positive coefficients after t=u+5.