Question 22Let $f(x)=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4$, where the coefficients are constants and $a_4\ne0$. When divided by $x-2003,x-2004,x-2005,x-2006,x-2007$, respectively, $f(x)$ has remainders $24,-6,4,-6,24$. Find $f(2008)$.