If a polynomial \(p(x) = x^2 - 3x - 88\) is divided by a polynomial \(q(x)\) we get \(\frac{x - 11}{x + 8}\), find \(q(x)\).
 
Answer:
 
The polynomial \(q(x)\) \(=\) iiiiiii
 
[Note: Enter the answer in the decreasing order of the variable.]