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/ f(x + 1) - f(x) = 6x + 4.
f(x + 1) - f(x) = 6x + 4.
February 22, 2026
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By the **Remainder Theorem**, the remainder is simply $ f(1) $.
f(1) = 1^3 + 2(1)^2 - 5(1) + 6 = 1 + 2 - 5 + 6 = 4.
So the remainder is:
Find $ f(x) $.
This is a finite difference equation. Since the difference is linear in $ x $, $ f(x) $ must be a quadratic polynomial. Let:
f(x) = ax^2 + bx + c.
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