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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)

D Deependra Verma

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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