2011/12 AHSMC Part 1 Problem 8

Note that $g(x) = f(x + 1) - f(x)$ is a linear polynomial. Since $g(1) = f(2) - f(1) = 2$ and $g(2) = f(3) - f(2) = 4$, we have $g(3) = 6$. Hence $f(4) = f(3) + g(3) = 8 + 6 = 14$. The answer is (B).