if the polynomials ax^3+4x^3+3x-4 and x^3-4x+a leave the same remainder when divided by (x-3) , find the value of a.

Answers (1)

solution: Let p(x)=ax^3+4x^2+3x-4  and  q(x)=x^3-4x+a be the given polynomials .

                 The remainder when p(x)  and  q(x)  are divided  by (x-3)  are  p(3)  and  q(3)  respectively.

                 By the given condition , we have 

                         p(3)=q(3)

Rightarrow                     a	imes3^3+4	imes3^3+3	imes3-4=3^3-4	imes3+a

Rightarrow                     27a+36+9-4=27-12+a

Rightarrow                    26a+26=0Rightarrow 26a=-26Rightarrow a=-1

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