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A polynomial f(x) of degree 4 satisfies f(1) = 1, f(2) = 2, f(3) = 3, f(4) = 4, and f(0) = 1. Find f(5).
- 5
- 6
- 7
- 8
Correct answer: 6
Solution
Since f(x) - x is zero at x = 1, 2, 3, 4 and has degree 4, it equals a(x-1)(x-2)(x-3)(x-4). The condition f(0) = 1 fixes a. Then f(5) = g(5) + 5.
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