Factorising (1 Viewer)

[ubermale]

It seems that every time I come back to school from holidays I lose the knack to factorise even the most simple expressions. The tips i've been given so far is to always extract any common factors first and then look for other things like difference of two squares etc. I would appreciate any other tips and ideas on how to approach expression when asked to factorise them, or if anyone had a step-by-step guide, flowchart or some other aid that would also be great.

Thanks in advance guys!

 

[x.Exhaust.x]

Get a textbook, and practice. Practice makes perfect.

 

[eliseliselise]

what method do you use??? i think "The Cross Method" rocks! and it's somewhat hard to forget, at my school they teach the other way and every one wastes time trying to re-remember it and attempting to actually execute it. also, do as many factorisations as you possibly can- coz factorisation is something you HAVE to be good at; its like the root of life to a lot of math things!!!

you should also just believe in yourself, and paint with all the colours of the wind.

good luck!!
and
long live the cross method!!

btw our british friend, beth has compiled a lovely word doc for this exact purpose!!!
http://www.bethsmaths.co.uk/Beths/Bridging Course 2004.doc
click here!!!

edit: copied the wrong link aaahahha..

 

[bored of sc]

for quadratic equations (e.g x^2 - 7x + 6) work out what two numbers multiply to give AC and add to give B (A is the number in front of the x^2, B is the no. in front of the x and C is the thrid number) so in the above example A = 1, B = -7 and C = 6; so therefore we are looking for 2 numbers that multiply to give 6 (A times C or 1 times 6) and 2 number that add to give -7 (B)
in this example the 2 numbers are -6 and -1 so then take those two numbers as two seperate B's x^2 - 1x - 6x + 6, now you are looking for common factors x(x - 1) - 6(x - 1) so the brackets are the same

so the question was x^2 - 7x + 6

and the answer is (x-1)(x-6)

okay, that probably didn't make any sense but um, yeah, its a really good method that works when explained properly

um, yeah, look for difference of two squares, perfect squares and common factors and all that stuff

but most of all, ask the teacher for as many methods as possible and to explain the concepts in as many ways as possible

 

[Aerath]

Any decent 2U or 3U textbook should have the first chapter as factorising.
You need to nail factorising ASAP. Nearly every topic will involve some form of factorisation, so it's better to know it now, rather than later.

 

[ubermale]

Thanks for the help.

I use the inspection method most frequently for quadratic trinomials and I also use bored of sc's method (I don't really like the cross method).

But my problem is that sometime I don't know what method to start off with, for example I have a question that says,

"Factor fully:

a^4 + 4b^4"

When I look at it I see it:
- has no common factors
- isn't difference of two squares
- isn't a perfect square
- isn't a sum/difference of two cubes
- isn't a cube of a sum/difference

So it's questions like this in particular that I'm finding difficult.

 

[I'm outrageus]

i think you need to complete the square for that question. i did it and got

(a^2 + 2*b^2) - 4*a^2*b^2

but i'm not too sure....

I'm not too sure either,but my teacher told me once this rule:

a^2+b^2=(a+b)(a+b)-2ab

so the answer to the previous question (a^4+4*b^4) could be:

(a^2+2*b^2)(a^2+2*b^2)-4*a^2*b^2

 

[I'm outrageus]

which is exacly the same as completing the square...

yes , the same result,just two different approaches to the question.. so we might be right

 

[Continuum]

yes , the same result,just two different approaches to the question.. so we might be right

It's not two different approaches though, it's exactly the same approach - your teacher just happened to give you the general equation for it.

 

[Mark576]

a^4 + 4b^4 = (a^2 + 2b^2)^2 - 4a^2b^2
= (a^2 + 2b^2 + 2ab)(a^2 + 2b^2 - 2ab) <---using the difference of two squares
= [(a+b)^2 + b^2][(a-b)^2 + b^2] for a more neat and concise factorisation.

You just need to expose yourself to a variety of questions in order to develop your methods and recognition of viable means to easily factorise. It's just PRACTISE, as always

 

[ubermale]

Thanks for all the help so far. I agree with what Mark576 said in terms of me having to expose myself to a wider variety of questions, it's just that the text book I'm using only has ten questions of this difficult nature, so I might have to find questions elsewhere.

 

[kaz1]

try cambridge that book is pretty hard for me

 

[Mark576]

The Cambridge Year 11 Extension Maths textbook has excellent questions on factorising in the extension section.