if f(X)=1+x+x^2+...........x^6 the remainder when f(x^7) is divided by f(x) is

• remainder will be 0.
• 10 years agoHelpfull: Yes(6) No(4)
• Ans is:0
  F(x)=1+x+x^2...x^6
  Take x=1
  F(x)=7
  F(x^7)=1
  F(x)/F(x^7)=7/1=7 Remainder 0
• 10 years agoHelpfull: Yes(4) No(3)
• Answer will not be 0.the only possibility is not taking x=1.but do take x=2,3..and you will find the answer that the remainder is 1.
• 10 years agoHelpfull: Yes(3) No(0)
• x^7+x^7+x^7+x^7+x^7+x^7
• 10 years agoHelpfull: Yes(1) No(3)
• ans:0.
  take x=1.
  then f(x)=7 and f(x^7)=7.So,answer must be 0.
  
• 10 years agoHelpfull: Yes(1) No(3)
• FOR F(X^7)=1+X^7+X^14+X^21+X^27+X^35+X^42
  aND f(X)=1+x+x^2+...........x^6
  
  Now:
  (1+X^7+X^14+X^21+X^27+X^35+X^42)=1+x^7((1-x^2)/(1-x)) USING G.P SERIES
  a((1-r^n)/(1-r))
  Similary for 1+x+x^2+...........x^6 =1+x^2((1-x^2)/(1-x))
  
  Expand 1-x^2=(1+x)(1-x)
  NOW SIMPLIFY
  we will get
  (1+x^7(1+x))/(1+x^2(1+x))
  NOW SUBSTITUTE 2,3,4,....
  we will get Remainder 0
  TAKE 2
  On Substitution x=-1 as its only eas
• 10 years agoHelpfull: Yes(1) No(2)