In this question, A^B means A raised to the power B.Let f(x)=1+x+x^2+......+x^6.Then reminder when f(x^7) is divided by f(x)is:
(a)6
(b)7
(c)0
(d)none

• Given that f(x7)=1+x7+(x7)2 + ....+ (x7)6 = 1+x7+x14+....+x42
  We will rewrite the above equation, f(x7)=1+(x7−1)+(x14−1)+... + (x42−1)+6
  We know that x7−1=(x−1)(x6+x5+...1)
  (∵ xn−an = (x−a).(xn−1+xn−2.a+xn−3.a2.....+an−1 )
  Now It is clear that x7−1 is exactly divisible by f(x).
  Also x14−1=(x7)2−12 and x7−1 is a factor of this expression. (∵xn−an is always divisible by x−a
  Similarly, we write x21−1=(x7)3−13, x28−1=(x7)4−14....
  So remainder = 1 + 6 = 7
  
  
• 8 years agoHelpfull: Yes(9) No(5)
• put x=1,f(x)=7 and f(x^7)=7 sof(x)/f(x^7) gives reminder=0
  
• 8 years agoHelpfull: Yes(7) No(9)
• ans will be 7
• 8 years agoHelpfull: Yes(2) No(1)
• 0 if we put x = 1
• 8 years agoHelpfull: Yes(2) No(1)
• D) none of the above
• 4 years agoHelpfull: Yes(0) No(0)