Let $a(x)=-6x^3+19x^2+8x+12$, and $b(x)=3x^2+x+1$. When dividing $a$ by $b$, we can find the unique quotient polynomial $q$ and remainder polynomial $r$ that satisfy the following equation: >$\dfrac{a(x)}{b(x)}=q(x) + \dfrac{r(x)}{b(x)}$, where the degree of $r(x)$ is less than the degree of $b(x)$. **What is the quotient, $q(x)$**? $ q(x)=$ [[☃ expression 1]] **What is the remainder, $r(x)$**? $r(x)=$ [[☃ expression 2]]