Final answer:
The quotient in partial fractions is 1 - (17/(x-3)) + (12/(x-2)), and the remainder is (7/(x-3)) - (5/(x-2)).
Step-by-step explanation:
To find the quotient and remainder in partial fractions, we can use the method of polynomial long division. In this case, the numerator is x^2 + 8 and the denominator is x^2 - 5x + 6.
By performing the long division, we get the quotient as 1 - rac{17}{x-3} + rac{12}{x-2} and the remainder as rac{7}{x-3} - rac{5}{x-2}.