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Divide polynomials with remainders: monomial divisors

Let a(x)=3x3+1a(x)=3x^3+1, and b(x)=x2b(x)=x^2.
When dividing aa by bb, we can find the unique quotient polynomial qq and remainder polynomial rr that satisfy the following equation:
a(x)b(x)=q(x)+r(x)b(x)\dfrac{a(x)}{b(x)}=q(x) + \dfrac{r(x)}{b(x)},
where the degree of r(x)r(x) is less than the degree of b(x)b(x).
What is the quotient, q(x)q(x)?
q(x)= q(x)=
What is the remainder, r(x)r(x)?
r(x)=r(x)=