Question 666619
Average rate of change from a to b  of f(x):   {{{(f(b)-f(a))/(b-a)}}}

{{{(f(x) - f(1))/(x-1) = (x^3 + x - 2)/(x-1)}}}

Use long division to arrive at the result:  

x-1 |  x^3+x-2

x goes into x^3 x^2 times

(x-1)x^2 = x^3 - x^2

x^2+x-2 is what's left.

x-1 | x^2 +x -2

x goes into x^2 x times


(x-1) * x = x^2-x

2x -2 is whats left.

x goes into 2x  2 times.

2*(x-1) = 2x-2

So there's nothing left (remainder of 0)

giving us x^2+x+2


x^2+x+2. Choice B