Given f(x) = 2x3 + px2 + qx + 1. When f(x) is divided by x+1, the remainder is 5. When f(x) is divided by x-2, the remainder is 5. Determine p and q.

Question 1.1:
Given $f(x) = 2x^3 + px^2 + qx + 1$.
When $f(x)$ is divided by $x+1$, the remainder is 5.
When $f(x)$ is divided by $x-2$, the remainder is also 5.
Determine the values of $p$ and $q$.

Step 1: Apply the Remainder Theorem for the first condition.
According to the Remainder Theorem, if $f(x)$ is divided by $x-a$, the remainder is $f(a)$.
For division by $x+1$, we have $a = -1$. The remainder