3.26: Polynomial factor and remainder

Show that $b = -9$.

It is also given that $3x + 2$ is a factor of $p(x)$ and that when $p(x)$ is divided by $x + 1$ the remainder is $6$.

Find the values of $a$ and $c$.

Find the quadratic $q(x)$ such that $p(x) = (3x + 2)\,q(x)$.

Hence find $p(x)$ as a product of linear factors with integer coefficients.