If 1 + x^4 + x^3 + x^2 + x = 80, then the average (arithmetic mean)R of x, x^2, x^3, x^4 and x^5 is equal to which of the following? Choose one
A) 12x
B) 13x
C) 14x
D) 16x
E) 20x
1 + x^4 + x^3 + x^2 + x = 81   i.e. 1 +x+ x^2+ x^3+ x^4 = 81   x+ x^2+ x^3+ x^4 = 80   x(1 +x+ x^2+ x^3) = 80   x(81-x^4) = 80   81x - x^5 = 80   x^5 = 81x -80   Now x+ x^2+ x^3+ x^4+ x^5 = 80 + 81x -80 = 81x   Average of R{x, x^2, x^3, x^4, x^5} 80 + 81  -80= 
<gadget id="calculator">80 + 81  -80</gadget>
<output>81</output>
81x   Average of R{x, x^2, x^3, x^4, x^5}= 81x/5 ~ 16x   Answer16x
<result>D</result>
If 1 + x^4 + x^3 + x^2 + x = 80, then the average (arithmetic mean)R of x, x^2, x^3, x^4 and x^5 is equal to which of the following?