Consider the polynomial $$p(x) = x^6 + 10x^5 + 11x^4 + 12x^3 + 13x^2 - 12x - 11.$$ Find the remainder when $p(x)$ is divided by $x+1$. [1 point]

For a natural number $n$, let $a _ { n }$ be the remainder when the polynomial $2 x ^ { 2 } - 3 x + 1$ is divided by $x - n$. Find the value of $\sum _ { n = 1 } ^ { 7 } \left( a _ { n } - n ^ { 2 } + n \right)$. [3 points]

The polynomial $P ( x ) = ( x + 1 ) + ( x + 2 ) + \ldots + ( x + 9 )$
$$Q ( x ) = ( x + 1 ) + ( x + 2 ) + \ldots + ( x + 5 )$$
is divided by the polynomial.
What is the remainder obtained from this division?
A) 10 B) 12 C) 14 D) 16 E) 18