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how can i find the remainder theorem and factor theorem to f(x)=4x^6-64x^4+x^3-19

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 Possible Rational Roots are : ±1 ,  ± 1 , ±19 , ± 19  , ±19
                                                  ±2     ±1       ±2     ±4
 
 
     Polynomial has root of X=1 if and only if Polynomial is divisible by  X-1
 
     Do the long division to determine that:
 
             4X 5 +4X4-60X3-59X2 +59X- 59                                -59X2- 19
  X - 1  l  4X6- 64X4+X3- 19                                                      -59X2 -59X
              4X6 -4X5                                                                             -59X -19
                4X5- 64 X4                                                                        - -59x +59 
                 4X 5- 4 X4                                                                                  -78
                      -60X4+X3                     f(X) = (X-1) (4X5 +4X4 -60X3-59X2 +59X -59
                      -60X4+60X3                   then f(1) = -78  the remainder.
                               -59X3- 19
                                59X3-59X2           f(1) = 4(1)6- 64(1)4+ (1)3 -19 =-78