1.6: Constants from remainders and divisibility

Given that $p(x)$ has a remainder of 2 when divided by $2x + 1$ and that $q(x)$ is divisible by $x + 2$, find the value of each of the constants $a$ and $b$.

Given that $r(x) = p(x) - q(x)$ and using your values of $a$ and $b$, find the exact remainder when $r(x)$ is divided by $3x - 2$.