if (x+1)is a factor of (xn+1)oniy if,
  1. n is an odd integer
  2. n is a even integer
  3. n is a negative integer
  4. n is a positive integer

Asked by my3shyll | 25th Jul, 2015, 07:56: PM

Expert Answer:

G i v e n space f open parentheses x close parentheses equals x to the power of n plus 1 F a c t o r space T h e o r e m colon space I f space f open parentheses x close parentheses space i s space d i v i d e d space b y space x plus 1 comma space t h e n space f open parentheses negative 1 close parentheses equals 0 f open parentheses x close parentheses equals x to the power of n plus 1 rightwards double arrow f open parentheses negative 1 close parentheses equals open parentheses negative 1 close parentheses to the power of n plus 1  f open parentheses negative 1 close parentheses equals 0 rightwards double arrow open parentheses negative 1 close parentheses to the power of n plus 1 equals 0 rightwards double arrow n space i s space a n space o d d space i n t e g e r. rightwards double arrow H e n c e space left parenthesis 1 right parenthesis space i s space t h e space c o r r e c t space o p t i o n.

Answered by Vimala Ramamurthy | 26th Jul, 2015, 02:31: PM