Question

# If ${x^{51}} + 51$ is divided by $x + 1$, Then the remainder is$A)0 \\ B)1 \\ C)49 \\ D)50 \\$

Here given polynomial is ${x^{51}} + 51$ and divided by $x + 1$
Remainder=$f( - 1)$ since the divisor is $x + 1$
$\Rightarrow f(x) = {x^{51}} + 51 \\ \Rightarrow f( - 1) = {( - 1)^{51}} + 51 \\ \Rightarrow f( - 1) = - 1 + 51 \\ \therefore f( - 1) = 50 \\ \\$
Hence the remainder is $50$