Prove

f(x)=x³ + x² + x + 1=(x² +1)(x+1)

Remainder on dividing g(x)=x^4p + x^4q+1 + x^4r+2 + x^4s+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.)