Final answer:
The question is about division of polynomials and finding the quotient and remainder, however, due to discrepancies in the provided details, a precise answer cannot be given without additional context or clarification regarding the original problem.
Step-by-step explanation:
The question seems to pertain to the concept of rewriting equations and finding the quotient (q(x)) and the remainder (r(x)) after division. However, based on the information provided, it appears there are some discrepancies in the question details, particularly since there are references to the quadratic formula and mathematical expressions that are not fully contextualized with respect to the original question about rewriting in the form q(x).
For a typical algebraic expression in the form of a polynomial divided by a binomial, we rewrite it by dividing through the polynomial to find the quotient and the remainder. The quotient (q(x)) is the result of the division without the remainder, and the remainder (r(x)) is what's left over.