f(x + 1) - f(x) = 6x + 4.

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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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