cross method of factorisation? (1 Viewer)

[saa]

Ok, I've been having a dumb moment for a while... Someone has asked me to explain quadratic factorisation (year 10 stuff), but I never learnt the cross method - always did it another way..

So is anyone able to give me a quick rundown on the cross method??
(used to factorise quadratics when 'a' > 1)

 

[saa]

Thanks. I did a bit of searching around on the net and found some similar info to what you said.

I'm fine with my method, but the guy who asked me to explain was taught the cross method, so I thought I might try here to find out an explanation, which I could then pass on.

I've since just found out it's another guess and check style of method, but didn't know that at first

What mainly threw me was say when 'a' = 6, cause then you have 2 sets of factors for it, plus the 2 or more for 'c' and I thought there might have been some trick with the cross method, but it's just another guess and check style - which of course with practice becomes quicker

 

[kpq_sniper017]

i've never used any methods other than the cross-method and the quadratic formula

what other methods are there??

 

[velox]

i use psf, although i learnt cross again for my half yearlies as its better

 

[saa]

By years of practices I can usually just look at it and figure it out. What multiplies to give 'ac' and adds to give 'b'

What's this 'psf' method?

 

[:: ck ::]

My graphing calculator (Ti Voyage 200)

Too bad you can't use that in ur assessments or in the HSC =P

 

[mojako]

What is psf?

I use this method (don't know the name, and would be glad if informed), for example,
ax^2 + bx + c
find 2 numbers whose sum equal b and product equal ac, I do this by
writing a and c in a row in seperate columns, then
multiplying (or dividing) both columns by certain numbers [can be up to several times] so that the new numbers (eg written in the next row) add up to b.
Let the numbers be e and f.
Then I write
(ax+e) (ax+f) / a
and that's it.

 

[:: ck ::]

ur "method" is pretty much what every1 does first when viewing a quadratic...

u shud b able to do it in ur head by now =\

unless its crazy with huge numbers in front ... which is when i just use quadratic formula..

 

[Winston]

Originally posted by :: ryan.cck ::
Too bad you can't use that in ur assessments or in the HSC =P

Yes you can... drop to general ...

 

[gman03]

In the end, you can still use completing the squares... That what I use all the time. Why? because I got no intuitions......

 

[kpq_sniper017]

there's a simple quadratic formula.
but just for interest, is there a simple cubic/quartic formula? i think i search for a cubic one and it was huge! too much to remember....it was like sqrt of a sqrt of a cube root.....lol
dunno about quartics though.

 

[Slidey]

The cubic formula would necessarily be an order of magnitude bigger than the quadratic formula, I guess. That's why you have the whole synthetic divison method, long divison method, remainder theorem and all the other polynomial methods to help you.

 

[CM_Tutor]

I posted the way to solve the cubic not that long ago in the Extension 2 forum - but I doubt anyone would call it 'simple'.

 

[kpq_sniper017]

Originally posted by CM_Tutor
I posted the way to solve the cubic not that long ago in the Extension 2 forum - but I doubt anyone would call it 'simple'.

so i guess the cubic formula isn't something u can quote in an exam....

is there a quartic formula? i'd like to see how big that one is

 

[gman03]

Originally posted by pcx_demolition017
so i guess the cubic formula isn't something u can quote in an exam....

One of the formula is called Cardan formula.

 

[Estel]

There is a general cubic and quartic formula.
None for any of a higher degree polynomial (not sure if it was proven that there wasn't one).

 

[sneaky pete]

yeah deadset with poly's with degrees 5 theres no 'general' equation (abels impossible thm.) althou some of them can be solved but the working out looks fugly

additionaly theres some weirdass method of solvng (some) polys with degree 6, i remember reading about it on the wolfram website

 

[mojako]

Originally posted by :: ryan.cck ::
ur "method" is pretty much what every1 does first when viewing a quadratic...

u shud b able to do it in ur head by now =\

unless its crazy with huge numbers in front ... which is when i just use quadratic formula..

Is there a name for it??

What's this "PSF" method?

 

[kpq_sniper017]

I would guess you could derive a formula for any degree polynomial if you had enough patience and persistence.

except for the quintic.

some guy proved that there is no general formula for a quintic