Factoring Limits: Solving Quadratic Equations

In summary, the conversation discusses the speaker's self-teaching of algebra and calculus, as well as their struggles in high school. They then ask for help with factoring limit questions, providing an example and indicating that they are aware of the quadratic equation but unsure of how to apply it in certain situations.
  • #1
PowerBuilder
11
0
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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  • #2
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) :)
 

FAQ: Factoring Limits: Solving Quadratic Equations

What is factoring and how does it relate to solving quadratic equations?

Factoring is the process of breaking down a polynomial into smaller parts, or factors, that can be multiplied together to get the original polynomial. In the case of solving quadratic equations, factoring allows us to find the values of x that make the equation equal to 0.

Why is factoring important in mathematics?

Factoring is important because it allows us to simplify complex expressions and solve equations. It is also a crucial step in finding the roots of a polynomial, which is essential in many applications of mathematics.

How do you factor a quadratic equation?

To factor a quadratic equation, we need to look for two numbers that, when multiplied together, give us the constant term of the equation and when added together, give us the coefficient of the x term. These two numbers will be the factors of the quadratic equation, and we can use them to rewrite the equation in factored form.

What are the different methods of factoring quadratic equations?

There are several methods of factoring quadratic equations, including the greatest common factor (GCF) method, the difference of squares method, and the quadratic formula. The method we use depends on the form of the equation and the factors involved.

How do factoring limits relate to solving quadratic equations?

In some cases, factoring limits can help us solve quadratic equations that cannot be solved using traditional factoring methods. By taking the limit as x approaches a certain value, we can find the value of the quadratic equation at that point, which can lead to solving the equation and finding the roots.

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