Mastering Factoring: Tips and Examples for Aspiring Physicists

[QuantumTheory]

Well my ultimate dream is to become a physicist. I have some other interests, such as being a pilot (flying a commerial airplane), since my vision is not 20/20 and I cannot fly in the airforce or navy. I also would like to create video games, and the colleage I would go to for that you learn calculus courses. In flying, you must know vectors.

It's really all fasinating.
But I have trouble with one of the most fundamentals of calculus; factoring.

Right now I'm not in school. You see, I went to a charter school (A school which you can go at your own pace, on computers) for a year. I graduated from 11th grade there. I failed the AIMS math test because I got frusterated over material I had no learned yet. (As a freshmen I took pre algebra, as a sohpmore I took algebra and as a junior I took more algebra and geometry).

Out of all this algebra, I never was taught factoring, or a good majority of what was on the AIMS math. I do GOOD in math, I've always had A's.

I graduated early; and I just moved to surprise arizona, so I am not enrolled in school yet. I'm waiting for 12th grade to start. I was supposed to have to take the math AIMS before I could go on to 12th grade (I failed it) but I moved BEFORE I could retake it.

I'm hoping to take trigonmetry but I'm scared I will be behind since I am having a lot of trouble factoring. I have a calculus book, and it talks about factoring.

It's confusing especially because I don't have a teacher to talk to. My parents are bad at math.

How do you factor something using the difference of squares such as:
2x^2 + 10. You can't factor 10, because its not a perfect square. Could someone please give me some examples, including the different types of problems, and then give me some problems, so I can solve them.

Thank you.

PS: I know I have a long ways to go but I hope to become a physicist.

 

[Data]

2x^2+10 cannot be factored over the reals. It is not a difference of squares, it is a sum of squares. A difference of squares is something of the form a^2-b^2, which factors to (a-b)(a+b). So, for example, 2x^2-10 = (\sqrt{2}x - \sqrt{10})(\sqrt{2}x+\sqrt{10}).

 

[whozum]

2(x^2+5) is as far as you can go on the real number line.

It fits the form of a^2+b^2 [/tex] which factors to (a+bi)(a-bi) [/tex] where i = \sqrt{-1} [/tex] but this is a complex number and is usually not what you are looking for.

 

[ek]

Physicist. Please.

And yes you will be far behind if you haven't done any trigonometry yet. That's grade nine material.

If I were you I'd be worrying about trig a little more since it is far more germane to the calculus than is factoring.

 

[QuantumTheory]

well, i know trig is not 9th grade level! that's ridiculous. no need to be cocky about it.

 

[blue_soda025]

Nobody's being cocky about anything here. But yes, you do start learning trig in gr 9. Or at least you do here.. (Canada). Obviously, it's very simple trig then, but still trig nonetheless. But yeah, you do need to know how to factor in a lot of things you do in math.

 

[ek]

well, i know trig is not 9th grade level! that's ridiculous. no need to be cocky about it.

In British Columbia, yes it is. Grade nine and ten.

 

[cepheid]

LOL...two BC guys chiming in on that point. I would too, just to be perverse and make it three BC guys, but that's extreme. Instead I'll say, cut the guy some slack. He's obviously young and enthusiastic. Why would you want to stifle that? In any case, to offer some encouragement: sometimes at the school level, whenever you get stuck in math, you wonder, if you can't even handle the basics, how you'll ever realize your goals. Sometimes I feel that way in 3rd year university too! But don't sweat the little stuff. Keep plugging away at it. If you are good at math overall, and have the drive, then what's stopping you, right? Maybe some people learned trig earlier than you did. Whatever. It's not like you're incapable of learning it. No need to worry excessively over your career prospects right now either. Enjoy life a little. High school was fun, but I wish I had enjoyed it even more, because now there is much less time to do so.

Edit: That having been said, trig is very important. So is the ability to talk to a teacher about the areas in which you need to get caught up. Now that you are enrolled in school in Arizona, will you be able to do that? If not, perhaps see about getting a tutor? If you were 60 and trying to learn basic math, I think everyone's reaction would be different. But when your whole life is ahead of you...I just don't see the logic of going on like it's the end of the world that most kids your age are ahead. Just talk to somebody about what you're deficient in, and who knows? Maybe they will have dealt with this situation before and will be able to see about getting you up to speed through extra lessons etc. There's always a way.

 

[xanthym]

.


Try the tutorial on Factoring available at the Web Site shown below:
Navigate thru its 11 lessons by clicking the "NEXT" button when finished with each page. Have patience, start with the most basic lesson, and proceed carefully thru all the material. (Some pages take longer to load, and require scrolling down the page to begin. Also, click "CRUNCH SOME", when indicated, to obtain practice problems to solve.)
http://www.coolmathalgebra.com/Algebra1/10FactDivPolys/01_what.htm


(Incidentally, it's spelled "physicist".)
~~

 

[Math Is Hard]

Quantum, you'll be fine. I didn't take any trig in high school so I had to pick it all up "on the fly" in pre-calc. Was it easy? No, I had to work my tail off! But I got it done and went on to have much success in my calculus classes.
Sometimes when something is difficult for me, I get bull-headed and decide I'll make it my strength instead of my weakness, and I focus very hard on it. Maybe you could do the same with factoring. Bear down on it and kick it's tail! Make it your specialty.

I had this really great calculus teacher and he once told us that when he started in calculus it was hard for him just like it was for us. I was surprised because he seemed so inherently gifted and he had a PhD in math. I thought that the stuff was just "natural" to him, yet he had run into problems just I did! He said the way he overcame it was to do every problem he could get his hands on. I thought this was great advice. Don't just do the homework, make up problems and see how far you can stretch. Ask questions about everything. And of course, these forums are a great place for getting answers.

 

[shmoe]

Shall I be the fourth from BC? It's possible that math is arranged rather differently in the States, and they don't see trig until later?

advice for Quantum-don't be afraid to go slow. You're not in school at the moment, so you can learn at your own pace and concentrate on comprehension rather than grades. Try to actually really understand the material before you leap ahead several chapters. Work out practice problems from whatever source you're using, and go seek out other sources if you feel you need more practice or alternate explanations.

 

[LeBrad]

Don't worry sonny, I didn't have trigonometry until 11th grade, and things turned out just fine for me.

 

[moose]

Listen, I also live in Arizona and I took the aims math test a few weeks ago. I am not trying to put you down at all, but you might want to think about retaking a few basic math classes. The aims test had nothing on it that was beyond quadratic equation, and that's saying a lot. It shouldn't have been a problem for you. Which high school are you goin into man?
One more thing to consider, what you have not been taught is really easy to learn and I guess you could do that quickly. I still wonder, what could you have done in algebra OTHER than factor O.O?

 

[The Reverend BigBoa]

Listen, I also live in Arizona and I took the aims math test a few weeks ago. I am not trying to put you down at all, but you might want to think about retaking a few basic math classes. The aims test had nothing on it that was beyond quadratic equation, and that's saying a lot. It shouldn't have been a problem for you. Which high school are you goin into man?
One more thing to consider, what you have not been taught is really easy to learn and I guess you could do that quickly. I still wonder, what could you have done in algebra OTHER than factor O.O?

After reading your post, I have to say, I was pretty much at a loss myself as to what he was learning in algebra?

Sure, you can't "factor 10" into an "easy" square root, but then there are always tools like "completing the square", which he seems to be completely unfamiliar with as well.

I completely agree with Cepheid that there's no sense in squashing good ambitions, but what DO they teach in algebra these days??

Well, anyways, enough of that. Quantum, son, when it comes to "learnin how to factor", one of the most important things will be exposure. The type that comes with doing A LOT of problems. I'm not talking 50 or a 100 either. I'm talking hundreds and thousands. The more the better until you really feel comfortable with knowing what to apply in any case. Of course, you need to learn the principles as well, but then you have to apply them. There are several ways to "factor", some work for pretty much everything, but become tedious and time consuming, where as some ways might be limited to the type of equation they work on, but will save a ton of time IF you recognize that it can be applied in a particular case.

There's plenty of information on the internet, and then there's always "self help" books, like Schaums and others. If you're truly intent on taking trig, then by all means, do it. But intend on also doing some serious "side studying" of factoring IN PARALLEL, by which I mean to be doing it on your own in addition to the trig, or better yet, in advance, if you have enough time to do so at this point.

 

[motai]

Hmm... I remember doing geometry in grade 9 (not even honors geometry due to a schedule conflict !), not trig (that I learned in 11th during precalc). I wouldn't really stress over it too much, just think of it as a another opportunity to learn something new. As long as you have the right mindset towards mathematics you should be okay. I initally felt trepidation too when I first took calc, but it wasn't too difficult because I had a good teacher. For instance, right now I'm at the end of a calc 1 class, and I already took the initiative to try to learn some more stuff (such as improper integration and other stuff) that wasn't covered in the original course. Of course, the rest of my classmates are chilling since the AP test is over, but I am determined to get through the rest of our book before graduation.

After around a year of diligence and hard work in that class, I can now pick up practically any calculus book, read it, and understand what it is saying (unless of course it is way over my head in which case I try to understand the prerequisites first). It all comes down to getting comftorable with the material, and the best way to do that is, like Math is Hard said earlier, work on any problems you can. When doing assigned homework, go extra and pick out some problems that aren't covered. Finish those problems, and check to see if there were any errors made and try to improve them.

Back in elementary school math was one of my weaknesses (comparative to science and english). Now it is a comparative strength (though I still am a little slow at the fast mental stuff) but I can solve higher-level equations like the rest of them. All it takes is perspective. Just don't get yourself down though, because there will always be people in your age group who may know far more advanced material. When that happens, instead of thinking yourself as inferior, try to get them to teach you stuff .

 

[Sempiternity]

In most public secondary schools, students are able to double up on their math courses per year. For instance, a freshman (9th grade) student may take algebra first semester (first half the school year) and take geometry the following semester (second half of the school year). This is probably why the AIMs test was considered trivial by most sophomore and junior students, in contrast to the plan that you received of one type of math per year (9th pre algebra -> 10th algebra -> 11th geometry/algebra).

Nevertheless, like everyone has continually been emphasizing, there's still plenty of time to learn what you need, especially if you are motivated. Until computers are given heuristic specialist AI systems, it might be best to stick with human instructors...