Question

119. The remainder when x power n +n divided by
X-1 is:

(1) n
(2)cannot be determined
(3)n +1
(4) O

with explanations​

Answer 1

Answer:

x^n - 1 is always divisible by x - 1.

Lets prove this.

let f(x) = x^n - 1.

Now, we know that when a polynomial f(x) is divided by x - a, the remainder is f(a).

Now, Divisor = x - 1.

Therefore, the remainder will be f(1).

Now, f(1) = 1^n -1

= 1-1 [Since, 1 raised to any power is always 1]

= 0

Hope that helps

Answer 2

Answer:

I think it should be 1

Becoz

${x}^{n + n } = {x}^{2n} - - - - - 1$

$x - 1 = 0 \\ x = 1$

Putting this value in 1,we get

${1}^{2n} = 1 \\ because \: anything \: raised \: to \: 1 = 1$

So remainder is 1