Let $a(x)=3x^4-2x^2+x+5$, and $b(x)=x^4+x^2+x+1$.
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]]