<s>[INST] Determine polynomial of $3$ degree real coefficients $f(x)$ such that $f(x) \vdots (x-2)$ and $f(x)$ dividing by $x^2-1$ have remainder $2x$ I need help in this problem.

Problem: Determine polynomial of $3$ degree real coefficients $f(x)$ such that $f(x) \vdots (x-2)$ and $f(x)$ divided by $x^2-1$ has remainder $2x$ and suppose $f(x)=x^3+ax^2+bx+c$.

 [/INST] Hint:
$f(x)=(x^2-1)(x-a)+2x$ and $f(2)=0$.  
Solve for $a$.
$f(x)=x^3-ax^2+x+a$.
</s>