The polynomials ax3+3*2-3 and 2*3-5x+a when divided by (x-4) leave the same remainder , find the value of 'a'.

     Let       f(x) = ax³ + 3x² – 3

      and      g(x) = 2x³ – 5x + a

      f(4) = a x 4³ + 3 x 4² – 3

               = 64a + 48 – 3

               = 64a + 45

 

         g(4) = 2 x 4³ – 5 x 4 + a

                = 128 – 20 + a

                = 108 + a

 

It is given that:

                    f(4) = g(4)

                 64a + 45 = 108 + a

                   64a – a = 108 – 45

                          63a = 63

                              a = 63/ 63 = 1

 The value of a is 1.