Question

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

Answer 1

Answer:

Q (x) is a polynomial of degree n−1.

Step-by-step explanation:

If n is odd, the equation

xn+1 have the root x=−1 and, cf. a corollary of the Bezout’s theorem,

the polynomial P(x)=xn+1

can be divided by x−(−1)=x+1:

xn+1=(x+1)Q(x)

where Q (x) is a polynomial of degree n−1.