Limit evaluation. (Please confirm my work)

[mateomy]

Evaluate:

$$\lim_{x \to 2}\,\frac{x^3-4x^2+7x-6}{x-2}$$


To evaluate this limit did some synthetic division to ultimately get the polynomial of
$$x^2-2x+3$$

and evaluating this as as $x\to2$ I ended up with a final answer of 3.

Can someone just confirm that this is in fact, the correct answer. I have nothing to check my work with and I am just making sure all my skills are in order before my final.

Thank you very much in advance.

 

[hgfalling]

Yes, this is correct. You could also use L'Hopital's rule to check, if you know about that.

 

[mateomy]

Awesome thanks. No, not quite at L'Hopital yet, next semester.