Let $a
eq 0$ and $p(x)$ be a polynomial of degree greater than 2. If $p(x)$ leaves remainders a and $-a$ when divided respectively by $x+a$ and $x-a$, then the remainder when $p(x)$ is divided by $x^2-a^2$ is :

Question

Let $a 
eq 0$ and $p(x)$ be a polynomial of degree greater than 2. If $p(x)$ leaves remainders a and $-a$ when divided respectively by $x+a$ and $x-a$, then the remainder when $p(x)$ is divided by $x^2-a^2$ is :

Aicharya · Accepted Answer

Let the remainder be $R(x)$, then $R(x)=P(x)+q$ Given, $\quad R(-a)=a \Rightarrow-P a+q=a$ $\ldots$ (i) and $R(a)=-a \Rightarrow P a+q=-a$\ldots$ (ii) On solving Eqs. (i) and (ii), we get $P=1, q=0$ $	herefore \quad R(x)=-x$

Let $a \neq 0$ and $p(x)$ be a polynomial of degree greater than 2. If $p(x)$ leaves remainders a and $-a$…

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