Question

Find the remainder when \((x^{51}+51)\) is divided by (x+1).

Answer 1

Let \(f(x) = x^{51} + 51 \)
By remainder theorem, when f(x) is divided by (x + 1), then the remainder = f(−1).
Putting x = −1 in f(x), we get
\(f(−1) = (−1)^{51} + 51 = −1 + 51 = 50 \)
∴ Remainder = 50
Thus, the remainder when \((x^{51} + 51)\) is divided by (x + 1) is 50.