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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.

 Feb 17, 2021
 #1
avatar+120129 
+1

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

 

 

cool cool cool

 Feb 17, 2021

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