Question 666619
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
f(x)=x³+x, find the average rate of change of f from 1 to x: 
f(x) - f(1)/(x-1) = {{{(x^3 + x - 2)/(x-1) = (x-1)(x^2+x+2)/(x-1) = x^2 + x + 2}}}
Note:x^3 + x - 2 ,  x = 1 a root 0r (x-1) a factor 
using Synthetic Divsion
1	1	0	1	-2
 	 	1	1	2
 	1	1	2	0
generates the factor
  x^2 + x + 2