hiiiiiii

 

There have beeen correct answers to this query already .. however lemme make things a bit more clear and neat ...

 

well ... now we know x² + x + 1 divides g(x²) and x²h(x²)

 

Also x² + x + 1 is (x-)(x-²)

 

So this means that  and ² must make g(x²) and x²h(x²) zero ...

 

Now, g(²) = g(⁴) = 0                ..... (1)

 

and,  ²h(²) = ^4.h(⁴) = 0     ...... (2)

 

Now ⁴ =    

 

And thus from (1) we get g() = 0

 

And from (2) we get .h() = 0 or since  is not zero

 

                      we have h() = 0

 

So, the correct answer is (a)

 

cheers

 

 

And so we get