So the remainder is:
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- is divided by $ t - 1 $.
- 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.
- f(x + 1) - f(x) = 6x + 4.
- Find $ f(x) $.
- This is a finite difference equation. Since the difference is linear in $ x $, $ f(x) $ must be a quadratic polynomial. Let:
