Factoring Limits: Solving Quadratic Equations

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SUMMARY

This discussion focuses on factoring limits in quadratic equations, specifically addressing the limit of the function as x approaches a certain value. The user successfully factored the limit of the equation Lim (x^2 - 5x - 6)/(x^2 - 4) to (x-3)(x-2). However, they encountered difficulty with the limit Lim (x^2 + 3x - 24)/(x^2 + 8) and sought guidance on factoring this expression. The discussion concludes that for this second equation, direct substitution of x = 4 is valid since it does not result in an undefined expression.

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PowerBuilder
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Okay so I've been teaching myself (with the aid of the mighty internet & several friends) algebra & now calculus. I have found that I didn't do too good at high school for various reasons. Some good...some not good. Anyway...

I have a (what is probably a basic question) about factoring limit questions. I understand that with an equation like below (which results in 0, you need to factor it)

Lim x^2 -5x - 6
x->2 ------------
x^2 - 4

factored it works out to (x-3)(x-2).

I can manage that. What is the approach taken when you have something like

Lim x^2 + 3x -24
x->4 ------------
x^2 + 8

I don't know what to do in a situation like this, I don't know how to break it into a (x a)(x b) situation. I hope this thread isn't looked at & thought 'what a twit' I should say that I am aware of the quadratic equation...
 
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In this problem you can actually just substitute [itex]x = 4[/itex] since the result is defined (no 0 in the denominator or an infinity anywhere) :)
 

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