Question 13The polynomial $P(x)=\sum_{k=0}^{64}a_kx^k$, where $a_j$ are real numbers for $j=0,\ldots,64$ and $a_{64}=1$ is such that $P(j)=10j$ for $j=1,2,\ldots,63$. Find the remainder when $P(66)+P(-2)$ is divided by $67$.