Question

If $(x^{51}+51)$ is divided by (x+1) then the remainder is
(a) 0
(b) 1
(c) 49
(d) 50

Answer 1

Let $f\left(x\right)=x^{51}+51$
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.
Hence, the correct answer is the option (d).