Factorising a Quadratic I still struggle

[monet A]

Hi.

It's late in the game for me to still be banging my head over this one, so I was hoping for some priceless tips from those who are doing it in their sleep.. PLeeeasse

I know I should remember the Quadratic formula better than I do, but I was encouraged not to resort to it too quickly and so I have pushed myself to pull the roots out of the equation without it except that I struggle with it almost every time.

So here's my questions -
1 Can anyone give me mnemonic or something so I can stop forgetting the QF ?

and

2. Is there a way to recognise off the cuff that I can't get the roots out without it before I try to ?

and

3. Can anyone give me a worked example of doing so with some help on the tricks of the trade because I still struggle and I shouldn't now. I am supposed to have been doing it like my signature for years ?


Thanks in advance.

 

[Maxos]

Are you really referring to $$ax^2+bx+c=0$$ ??

 

[EnumaElish]

1 Can anyone give me mnemonic or something so I can stop forgetting the QF ?

$$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

You live in a house with a ground floor and a basement. On the ground level the first room belongs to Bill, who has a very NEGATIVE personality. Bill's room doesn't have a ROOf. The next room has a ROOf; you don't feel strongly positive or negative about that room. Three people live in that room: Brandon, who is a square guy; and the couple Annie and Charlie, FOR whom you could make a NEGATIVE remark. The basement is leased TO Amy.

 

[monet A]

Are you really referring to $$ax^2+bx+c=0$$ ??

Why? How bad is my terminology ?

Yeah I am. Do you have any handy factorising tips.

Heres what I can do:

if I have $2x^2 - 3x - 2$ then I can see that my factors need to be (x+a)(x-b) to get -2, and I know that a and b must have a product of -2 and 2x*b + x*a will need to have a sum of -3x.

But I still struggle with the rest using trial and error. I am sorry if I don't seem to be talking sense. I know what I need but it seems that everyone has their own name for it depending on what text they learned from or that I am just speaking greek to indians..
:tongue:

 

[quasar987]

You only have to remember the QF to find the factorisation of a quad. polynomial. Here's how it works:

Given a quadratic polynomial, if you find the zeros to be 'a' and 'b', and you suppose (without loss of generality) that its factorisation is of the form (x-A)(x-B). Then the zeros of this polynomial are A and B (cuz when you plug x = A or x = B, you get 0). But you know for a fact that the zeros of this polynomial are a and b. Hence, A = a and B = b. So finding the zeros of a polynomial is finding its factorisation!

 

[BobG]

Would it help if you knew a song about the quadratic formula?

http://www.calculus-help.com/funstuff/qformula.wma

Caution: This song includes descriptions of violence and murder. (but I think it was gratuitously inserted just to lure poor unsuspecting souls into listening to this god-awful song).

The song is from Michael Kelley's Calculus Help page.

Recognizing you have an easy root is more familiarity with elementary school arithmetic than anything else. Nothing sophisticated, just working with numbers enough that you can recognize which two numbers would give you both the sum and the product you desire.

 

[monet A]

Recognizing you have an easy root is more familiarity with elementary school arithmetic than anything else. Nothing sophisticated, just working with numbers enough that you can recognize which two numbers would give you both the sum and the product you desire.

Thankyou Bob. That song is AWful yes but it could be helpful.

On what you wrote above, also thankyou, perhaps my elementary arithmetic skills leave something to be desired. :grumpy: And that is my main trouble with it. I have tried practising superfluously as per the adage that it's the only way, but I just didn't seem to be getting better as I went along, sad huh?? Somehow I just have trouble getting past having three or more tries to get it right. I suspect I might just need to get used to the wrist slapping that I'm going to be in for through my dependence on the Quadratic Formula for now.

Thanks anyway for your help.

 

[Fermat]

I always found it simpler to remember some formulae by remembering how do derive the expression. So if I forgot it, or wasn't sure, then I would work it out!
Do you know how to work out the QF by completing the square?
Do that a few times until you're familiar with it.Then the next time you forget the QF, work it out.

 

[BobG]

Thankyou Bob. That song is AWful yes but it could be helpful.

On what you wrote above, also thankyou, perhaps my elementary arithmetic skills leave something to be desired. :grumpy: And that is my main trouble with it. I have tried practising superfluously as per the adage that it's the only way, but I just didn't seem to be getting better as I went along, sad huh?? Somehow I just have trouble getting past having three or more tries to get it right. I suspect I might just need to get used to the wrist slapping that I'm going to be in for through my dependence on the Quadratic Formula for now.

Thanks anyway for your help.

I'm not sure how long you've been factoring quadratic equations, but your problem doesn't sound that unusual. I always started with the middle term and had to write the numbers that added up to it off to the side so I could remember I'd covered that combination (it's a different format, even though it should be easy, so it throws you off for awhile).

 

[monet A]

I'm not sure how long you've been factoring quadratic equations, but your problem doesn't sound that unusual. I always started with the middle term and had to write the numbers that added up to it off to the side so I could remember I'd covered that combination (it's a different format, even though it should be easy, so it throws you off for awhile).

It's good to know I'm not alone. :tongue2:
How long I've been working with quadratics is; I missed out on the High school preparation and have been factorising them in college level problems for two years of part time study. I said above that I am *supposed* to be doing it like my signature, but I maybe should correct that to say that the level I am working at is *expecting* of that I don't struggle with this part of the problem. The frustrating thing is that it takes up time that I can't really afford in an exam process because I am already a slow methodical worker in the subject. Its frustrating to spend so long on adding and mutiplying different combinations of small numbers not to mention how it is sometimes when it takes me several times longer to factor than it does to do the other 85% of the problem, I know I end up missing marks that I could get otherwise. What a sulk I am. :uhh: I am making more of it than it is probably, I can always use the QF when I remember it.. sorry to carry on so.
I accept that if there is nothig much more to getting it right than I already know then I resign myself to working harder at it and depending of the QF in the mean time.

One other thing that I just thought of. Have I maybe been practising my factoring on the wrong examples, should I get a High school textbook and work through it. Would it be any much different or good for practise and building memory recognition than the problems in college level? Do you think?

 

[Learning Curve]

Are you really referring to $$ax^2+bx+c=0$$ ??

That's General Form not Quadratic Form