Question

How do you find the limit of `(x^3 - 7x + 6) / (3x - 3)` as x approaches 1?

Answer 1

`-4/3`

Explanation:

Factor:

To factor `x^3-7x+6` you can use the Possible Rational Roots Theorem which says the possible values of `x = +-1, +-2, +-3, +-6` , then you can use Synthetic Division to figure out which ones are zeros. Or you can find a zero by graphing `x^3-7x+6`:
graph{x^3-7x+6 [-16.01, 12.48, -1.94, 12.29]}:

`lim -> 1 (x^3-7x+6)/(3x-1) = lim -> 1 ((x+3)(x-1)(x-2))/(3(x-1))`

Cancel the `(x-1)` terms:
`lim -> 1 ((x+3)(x-2))/(3)`

Plug in `x = 1`: `lim -> 1 ((x+3)(x-2))/(3) = ((4)(-1))/3 = -4/3`