When the polynomial p(x)=Ax^21+Bx^17+Cx^9+3 is divided by x-5 the remainder is -2. find the remainder when P(x) is divided by x+5.

Using  the Remainder Theorem, this  means  that

A (5)^21  + B(5)^17  + C(5)^9   +  3   =  -2 

A(5)^21  +  B (5)^17  + C(5)^9   =   -5

And  when divided  by x  +  5 ,  this means that

A(-5)^21  + B(-5)^17  + C (-5)^9  +  3   =

-A (5)^21  -  B(5)^17  - C(5)^9  +  3     =

-   ( A(5)^21  + B(5)^17  + C(5)^9 )  +  3   =

-  ( -5)   +    3    =

5  +  3     =

8