In this question A^B means A raised to the power B. let f(x)= 1+x+x^2+...x^6. The remainder when f(x^7) is divided by f(x) is:
a) 7
b) 0
c) 6
d) none of these

• ans d none of these
  
  f(x^7)= 1+ x^7 + (x^7)^2 + .... + (x^7)^6
  = 1+x^7 + x^14 + .... + x^4 = 1+x^7 * (1+x+x^2 + ... +x^6)
  = 1+ x^7 f(x)
  f(x^7)/f(x) = (1+ f(x)*x^7 ) / f(x)
  the remainder is 1
• 9 years agoHelpfull: Yes(21) No(21)
• There is a pattern.
  if , f(x) = 1+x+x^2+.....+x^(n).
  for x > 1,
  then the remainder when f(x^(n+1)) is divided by f(x) is (n+1).
  so , here remainder is 7.
  
• 9 years agoHelpfull: Yes(12) No(5)
• to find remainder of a polynomial fn f(x)/g(x)
  put x = 0,1 or any value
  
  put x=0
  f(x)=1
  f(x^7)=1
  f(x^7)/f(x)= 1/1 => remainder = 0
  
  put x=1
  f(x)=7
  f(x^7)=7
  f(x^7)/f(x)= 7/7 => remainder = 0
  
• 9 years agoHelpfull: Yes(8) No(6)
• remainder is 0.
  at x=1
  f(x^7)/f(x)=1
• 9 years agoHelpfull: Yes(4) No(5)
• ans d none of these
  
  f(x^7)= 1+ x^7 + (x^7)^2 + .... + (x^7)^6
  = 1+x^7 + x^14 + .... + x^4 = 1+x^7 * (1+x+x^2 + ... +x^6)
  = 1+ x^7 f(x)
  f(x^7)/f(x) = (1+ f(x)*x^7 ) / f(x)
  the remainder is 1
• 9 years agoHelpfull: Yes(1) No(11)
• remainder for f(x^1) is 1
  and for f(x^2) is 2
  than similarly,
  for f(x^7) is 7
  hence 7 is the answer
  
• 9 years agoHelpfull: Yes(1) No(2)
• d..
  let x=1..
  then f(x)=7..
  and
  f(x^7)=8..thus we get,,
  f(x^7)/f(x)=8/7=1
  thus option is d
• 9 years agoHelpfull: Yes(0) No(2)
• ans d none of these
  
  f(x^7)= 1+ x^7 + (x^7)^2 + .... + (x^7)^6
  = 1+x^7 + x^14 + .... + x^4 = 1+x^7 * (1+x+x^2 + ... +x^6)
  = 1+ x^7 f(x)
  f(x^7)/f(x) = (1+ f(x)*x^7 ) / f(x)
  the remainder is 1
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• 9 years agoHelpfull: Yes(0) No(0)
• plzzzzzzzzzzzzzzz
• 9 years agoHelpfull: Yes(0) No(0)