The AC Method

I am an eighth grader taking ninth grade math, and I would like to have someone explain to me the AC method. Currently learning about factoring, and, as my recent homework shows, I am not exactly a master. I absolutely hate having to guess and check. Because of it my math homework takes much longer to finish than usual. But today in class, one of my friends mentioned something that his brother taught him called the "AC method" to the teacher as an alternative to factoring. Our teacher said he would not be teaching this to us, and so now I have two choices: wait until I am taught it, or learn a little bit of advanced math before I'm supposed to. Being the inquisitive person I am, I have chosen the latter. So, in conclusion, can anyone teach me the AC method? And does it take less time to do than factoring?

I would be most grateful for any help.

AC Method is used for equations in the form of ax^2 + bx + c.

I never took eigth grade math here before, and I am not sure if it's good to learn it before your teacher teaches it to you. However, it's the best way to factor things, so I Googled it and found a very nice tutorial about it. That site explains it well, and if you are still having problems say it and I can help you a bit more on it.

Not quite, I believe, although I've never heard of an 'AC' method. I'll venture a guess.

When factoring, you try to get to (ax + b)(cx + d). 'AC' is in there... acx^2 + adx +bcx + bd

However, I don't know how that's helpful. There are certainly shortcuts in factoring, but there's not really a way to get around the guessing. Of course, you don't need to write out those big tables of numbers. It is best to think carefully about the numbers you are given. Assuming you have all common factors already separated, it isn't all that difficult.

Thank you both very much. That tutorial was very helpful, and Scott, I don't believe I've ever seen a anything like that before, though I am quite curious to see if it works. I suppose I should have just googled "AC method" myself, but I was afraid that I would find nothing (quite foolish) or I would find something with incorrect information.

No, I probably should not learn things before they are taught to me, but I have a curious nature. That, coupled with the fact that I am extremely impatient, tends to make me want to learn as much as I can, as quickly as possible. This could probably cause problems for me in the future, but so far I've had no trouble.

Anyway, thank you once again.

don't go looking for the easy way out when it comes to mathematics...there are many ways to go about doing each problem, but you should stick to how the teacher tells you. my teachers say do this problem a specific way on homework, test, and quizzes. if you do it a different way but get the right answer, they marked it wrong.

you maybe slow at you're homework right now, but you will soon recognize which way to do it just by practicing. then you will get quicker.

I didn't have much difficulty with Factoring...well, looking at the page for the AC method, it's a lot like the one my teacher taught me. Here is the way I do it..."The Magic Square Method":

1.Draw a box. I can't remember the actual numbers for each box, but numbers would be a bit confusing anyway without my notes from class with me. Separate the box into nine smaller boxes, and it should look like this:

 _____
|a|b|c|
|d|e|f|
|g|h|i|

In the box, ab =c, de=f, gh=i, gd=a, eh=b, fi=c, and f+i = b in ax^2+bx+c=0.
Don't worry, it's not very complicated.

2. fill box a with ax^2, and fill box b with c from the equation.

3. Multiply boxes a and b and put the product in box c.

4. with the product in box c (acx^2), find the factors of ac that when added equal b. In this method you don't have to write all of the factors down, so I guess that's one difference.

5. Fill box d with the highest factor of box a that box f can be divided by, and fill box e with the other factor, which should be able to be divided from box b.

6. Do the same with boxes g and h using i.

7. the two binomials use boxes d, e, g, and h, and are written as follows: (g+e)(d+h).

With this way, it takes only 5 lines, one to write the problem, three for the box, and a fifth for the factored form. With solving for x, it takes at least 6, depending on if you have to show your work solving with the Zero Property.

EDIT--and no need to answer, but why does everyone call it 9th grade math? Sure, it is taken in 9th grade by many, but even here in the county I live in in Georgia, I believe more than a third of the students take Geometry in 9th.

Originally Posted by daydreamer

don't go looking for the easy way out when it comes to mathematics...there are many ways to go about doing each problem, but you should stick to how the teacher tells you. my teachers say do this problem a specific way on homework, test, and quizzes. if you do it a different way but get the right answer, they marked it wrong.

you maybe slow at you're homework right now, but you will soon recognize which way to do it just by practicing. then you will get quicker.

Though I was wondering if this was simpler than normal factoring, I mostly just wanted to know what the AC method was. As I stated before, I have an insatiable curiousity. This would have bugged me for weeks had I not investigated. I am actually quite adept when it comes to math, and I can finish my homework quickly. I guess that's what happens when your dad is an accountant.

My teacher doesn't even grade our homework himself, anyway. He makes us trade with other people. Which, in my opinion, is a terrible idea. I'll bet that half the grades in my class are much better than they should be.

And besides, there was also the chance I would not be taught it in the years to come.

Ascalion, I can honestly say that I have never before heard of this "Magic Square Method." Judging from the instructions and your testimony, though, it seems as though it would work. Perhaps I'll mention it in class.

I just called it 9th grade math because, in my school district, that's what it would be. Now, I probably should have thought to myself, "But not everyone in the world is in my school district," but I did not. Very sorry for any confusion.