Asked by  | 6th Sep, 2008, 09:32: PM

Expert Answer:

f(x)=x3 + x2 + x + 1=(x2 +1)(x+1)

Remainder on dividing g(x)=x4p + x4q+1 + x4r+2 + x4s+3 by f(x) is :

g(-1)=(-1)4p + (-1)4q+1 +(-1)4r+2 +(-1)4s+3=0 for p,q,r,s being natural consecurtive numbers.Hence g(x) is divisible by f(x).(g(i)=(g(-i)=0 can be proved in similar way.)

Answered by  | 15th Dec, 2008, 02:39: AM

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