# Different Way to Solve a Limit of an Indeterminate Equation

$$lim_{x\rightarrow-2}\frac{x^3 + 8}{x+2}$$

Ok, I have solved this using synthetic division in which the limit was 12, however I was wondering if there was a way to solve this without using synthetic division (seeing as I hate the process of it).

I've solved plenty of other indeterminate equations by factoring out a polynomial and then being able to cancel out so that I can then plug in x, but I wasn't able to do so with this one.

I'm just curious if there are any other ways to solve this specific limit.

Thanks

Related Calculus and Beyond Homework Help News on Phys.org
L'hospital rule (applies only when it is in forms like 0/0, inf/inf)

differentiate both num and den, and then sub in your -2

Yeah I started reading up on that rule, but didn't understand it fully until your reply. So the derivative of the numerator is 3x^2 and the denominator is 1 so then just sub in the -2 and you get 12. Got it, thanks a lot for clearing up that rule for me.

dynamicsolo
Homework Helper
Not that this is much different than using synthetic division, but the numerator is a sum of two cubes, which factors according to

$$a^3 + b^3 = (a + b) \cdot (a^2 - ab + b^2)$$ . So, in fact, this numerator can be factored and the (x + 2) term can be cancelled.

Last edited: