CEMC Cayley, 1998

Algebra Difficulty 3.0 AMC 10/12 Find the answer Canada

When Betty substitutes $x = 1$ into the expression $ax^{3} - 2x + c$ its value is $-5$ . When she substitutes $x = 4$ the expression has value 52. One value of $x$ that makes the expression equal to zero is

(A) $2$ (B) $\dfrac{5}{2}$ (C) $3$ (D) $\dfrac{7}{2}$ (E) $4$

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