Question

Prove that x+1 is A factor of xn+1 where N is an odd positive integer

Answer 1

Answer:

See the detailed explanation

Step-by-step explanation:

• Factor theorem :  $(x-a)$ is a factor of polynomial $P(x)$ if $P(a)=0$

Here divisor $=x+1=x-(-1)$ and $P(x)=x^n+1$

$\Rightarrow P(-1)=(-1)^n+1$

And we know that if n is odd then $(-1)^n=-1$ and if n is even then $(-1)^n=1$

Thus for $P(-1)=(-1)^n+1$ to be zero, n  must be odd positive integer

Hence proved