If x^ 51 + 51 is divided by x + 1, the remainder is: - Vidyadip

Question

If $x^{51} + 51$ is divided by $x + 1,$ the remainder is:

✓

Answer

When the polynomial $p(x)$ is divided by $q(x)\ i. e. (\text{x}\pm\alpha)$ then $\text{p}(\mp\alpha)$ is the remainder.
If $\text{x}\pm\alpha$ is the factor of polynomial, then remainder is $'0\ '.$
So,
If $x^{51} + 51$ is divided $x + 1$.
Remainder $= (-1)^{51} + 51$
$= -1 + 51$
$= 50.$

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