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Problem 11 - Entrance Test

If f(x) = x^3 + ax^2 + bx + c, and f(1) = 1, f(2) = 2, and f(3) = 3, what is f(4)?

Correct: C

Let g(x) = f(x) - x. Then g(1) = g(2) = g(3) = 0. So g(x) = (x-1)(x-2)(x-3). Thus, f(x) = (x-1)(x-2)(x-3) + x. Then f(4) = (4-1)(4-2)(4-3) + 4 = 3*2*1 + 4 = 6 + 4 = 10.