What I tried :
I felt that $f(x) - x^3$ can give me the value of the quadratic part of the polynomial. As a result, taking the quadratic part to be of the form $ax^2 +bx + c$, the differences I get are :
- $f(1) - 1^3 = a + b + c = 0$
- $f(2) - 2^3 = 4a + 2b + c = -4$
- $f(3) - 3^3 = 9a + 3b + c = -18$
I am not an expert at solving 3 linear equations in 3 variables , but I tried and ended up pulling out my hair (trying to be a bit literary; hope you won't mind the wordings , but rather concentrate on the question). I tried to take 2 equations at a time, and ended getting multiple values for the same variables.
I will be grateful to anyone who is willing to help me out.