Question

see the Q and ans as fast as possible

Answer 1

                                       ☺☺☺

f ( x ) = x^5 - a^2 x^3 + 2x + a - 3

g ( x ) = x - a.

Since, given that g ( x ) is factor of f ( x ), so the zero of g ( x ) will be also the 
zero of f ( x ).

   x-a  = 0
 
   x = a. 

Zero of g ( x ) is a.

Now, 

  f ( x ) = x^5 - a^2 x^3 + 2x + a - 3

  f ( a ) = a^5 - a^2 * a^3 + 2a + a - 3 = 0

              a^5 - a^ ( 2 + 3 ) + 3a - 3 = 0

              a^5 - a^5 + 3a - 3 = 0

             0 + 3a - 3 = 0

                3a = 3

                  a = 3/3

                  a = 1.

So, when the value of a is 1, then ( x - a ) is a factor of ( x^5 - a^3 * x^3 + 2x + a - 3 )

                

                                              ☺☺☺