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 :
o 7
o 0
o 6
o None of the other 3 choices

• It is given f(x)=1+x+x^2+.........+x^6
  So f(x^7)=1+(x^7)+(x^7)^2+.......+(x^6)^7
  =1+x^7+x^14+............+x^42
  =1+(X^7 - 1)+(x^14 - 1)+..............+(x^42 - 1) + 6
  
  We know that (x^7 - 1)=(x-1)(x^6 + x^5 +x^4 + .....+1)
  So here (x^7 - 1) is divisible by f(x), because value of f(x) is (x^6 + x^5 +x^4 + .....+1)
  Simillarly (x^14 - 1),(x^21 - 1),......(x^42 - 1) ,all are divisible by f(x), because all of these contain
  (x^6 + x^5 +x^4 + .....+1).
  so f(x^7)/f(x)=
  
  ={1+(X^7 - 1)+(x^14 - 1)+..............+(x^42 - 1) + 6}/f(x)=1+x+x^2+.........+x^6
  so all term except 1 and 6 is divisible by f(x).
  so remainder is 1+6=7.
• 8 years agoHelpfull: Yes(10) No(0)
• 0
  SUB 1 IN F(X) AND F(X^7)
• 8 years agoHelpfull: Yes(3) No(7)
• 7 is the corret answer.
  bcz f(x^7)=7
• 5 years agoHelpfull: Yes(1) No(0)