Problem related to remainder A polynomial in $x$ leaves a remainder $2$ and $3$ when divided by $x-1$ and $x+1$. What is the remainder, when divided by $x^2-1$ ?
Hint.  The remainder will be a linear polynomial, say $ax+b$, and you need to determine $a$ and $b$.  The division can be written as
$$f(x)=(x^2-1)q(x)+ax+b\ .$$
From the given information you have
$$f(x)=(x-1)r(x)+2\ .$$
Now substituting $x=1$ in these two equations will give some information about $a$ and $b$, and you can use the other given remainder in a similar way to get a second equation.  You can then solve for $a$ and $b$.
Let $\displaystyle f(x)=(x^2-1)g(x)+A(x-1)+B(x+1)$ where $g(x)$ is a polynomial and $A,B$ are constants 

Using Polynomial remainder theorem, $\displaystyle2=f(1)=B\cdot(1+1)\iff B=1$

Similarly,  $\displaystyle3=f(-1)=A(-1-1)\iff A=?$