Since 24x2+25x−47 divided by ax−2 is equal to −8x−3 with remainder −53,it is true that (−8x−3)(ax−2)−53=4x^2+25x−47. (This can be seen by multiplying each side of the given equation by ax − 2). This can be rewritten as −8ax2+16x−3ax=24x2+25x−47. Since the coefficients of the x2 -term have to be equal on both sides of the equation, −8a=24, or a=−3. Choices A, C, and D are incorrect and may be the result of either a conceptual misunderstanding or a computational error when trying to solve for the value of a.