SAT Mathematics Practice Test 3

Since $24{\mathit{x}}^2+25\mathit{x}-47$ divided by $\mathit{a}\mathit{x}-2$ is equal to $-8\mathit{x}-3$ 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 $-8\mathit{a}{\mathit{x}}^2+16\mathit{x}-3\mathit{a}\mathit{x}=24{\mathit{x}}^2+25\mathit{x}-47$.
Since the coefficients of the ${\mathit{x}}^2$ -term have to be equal on both sides of the equation, $-8\mathit{a}=24$, or $\mathit{a}=-3$.
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.