Question

if x^41 + 41 / X + 1 then what will be the remainder

Answer 1

using remainder theorem

x^41+41

=(-1)^41+41

=-1+41

=40

so the remainder will be 40

Answer 2

The remainder is 40.

Given:

A polynomial ${x}^{41} + 41$ is divided by $x + 1$

To Find:

The remainder.

Solution:

To find the remainder we will follow the following steps:

As we know,

(x + 1) divides the polynomial which means the value at the value of x = -1 we have to find the remainder.

Now,

On putting values of x = -1 we get,

${ (- 1)}^{41} + 41 = - 1 + 41 = 40$

Odd power of -1 gives the same value i.e -1.

Henceforth, the remainder is 40.

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