Question 25
Let $h(k)=b_0+b_1k+b_2k^2+b_3k^3+b_4k^4+b_5k^5$ be a polynomial in k, where $b_0,b_1,b_2,b_3,b_4$ are constants and $b_5=7$. When divided by $k-2004,k-2005,k-2006,k-2007,k-2008$, $h(k)$ leaves remainders $72,-30,32,-24,24$ respectively. Determine $h(2009)$.
