Definition of deriviative, factoring problem

[gabby989062]

Homework Statement

use definition of derivitiave to find f'(c) EXACTLY
x3 - 4x2 + x + 8, c=1

Homework Equations

lim x->c f(x)-f(c) / x-c

The Attempt at a Solution

I got as far as (x3 - 4x2 +x + 2) - 6 / x-1

Plugging in 1 for x gives me divided by zero. The teacher's example, she factored an x-1 in the numerator and canceled it with the denominator, but she did an easy example that only had x2, and I have x3. How do I find an x-1 in the top?
:zzz:

 

[atqamar]

Simplify the numerator, and try factoring first two terms, and then the next two terms.

 

[HallsofIvy]

By the way, it is much easier to read what you really mean if you use "^" to indicate powers: x^3- 4x^2+ x+ 2, rather than x3-4x2+x+2.

x^3- 4x^2+ x+ 2- 6= x^3- 4x^2+ x- 4= (x-1)(?).

Knowing that one factor must be x- 1 should make that easy- just divide x^3- 4x^2+ x- 4 by x-1. If you use "synthetic division" it's even easier.