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Divide polynomials with remainders: binomial divisors

a(x)=x2+x+1a(x)=x^2+x+1, and b(x)=x1b(x)=x-1.
We can rewrite a(x)b(x)\dfrac{a(x)}{b(x)} as
q(x)+r(x)b(x)q(x) + \dfrac{r(x)}{b(x)}
where qq and rr are polynomials and the degree of rr is less than the degree of bb.
What is the quotient, q(x)q(x)?
q(x)= q(x)=
What is the remainder, r(x)r(x)?
r(x)=r(x)=