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Which method do you use to factorise hard quadratics?

Poll

Which method do you use?

As a tutor I have come across lots of weird and wonderful methods used by students to factorise quadratics where the 'a' coefficient is > 1 e.g.

6x2+13x+66x^2 + 13x + 6

Which method do you use? Take part in the poll or post below if your method isn't listed - I'm always interested to hear about new methods and it's nice to have all the different methods in one place so students can choose their favourite :smile:

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Some brief notes on the methods I've given so you can identify them.

Methods

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The quadratic formula.

Or is that not GCSE?
(edited 4 years ago)
I find inspection works best for me, but the a-levels calculator has given me the luxury of it doing everything for me :lol:

We only ever got taught the inspection/trial and error method in school so I find the AC methods really interesting!
depends on the question. if it says to give to significant figures then i do quadratic formula else i do complete the square or something
Reply 4
Avatar for Notnek
Notnek
OP
21
Original post by PepeTheFroggi
depends on the question. if it says to give to significant figures then i do quadratic formula else i do complete the square or something

I mean if a question just says "factorise this quadratic" so no solving equations.
Original post by Sir Cumference
I mean if a question just says "factorise this quadratic" so no solving equations.

aah whoops didnt read. then id do complete the square
Don't think mine is listed :s-smilie:
First I have to choose the 2 number that make 4x^2 !!!
20191201_135229.jpg
Original post by Sir Cumference
I mean if a question just says "factorise this quadratic" so no solving equations.

It won't though and even if it did you can always use the formula and convert your answers. (x - a)(x - b) and multiply up.
Reply 8
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Notnek
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Original post by Obolinda
Don't think mine is listed :s-smilie:
First I have to choose the 2 number that make 4x^2 !!!
20191201_135229.jpg

That's the inspection/trial and error method I mentioned :smile:
Original post by Sir Cumference
That's the inspection/trial and error method I mentioned :smile:

Oh:colondollar:

Original post by ghostwalker
The quadratic formula.

Or is that not GCSE?

We do use the quadratic formula (that's the calculator method) but paper 1 is non calculator so we need to be able to factorise(not just solve) without.
Original post by laurawatt
I find inspection works best for me, but the a-levels calculator has given me the luxury of it doing everything for me :lol:

We only ever got taught the inspection/trial and error method in school so I find the AC methods really interesting!

I got the inspection method from my teacher and the AC method from Mathswatch - it is very long!
Reply 11
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Notnek
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Original post by Muttley79
It won't though and even if it did you can always use the formula and convert your answers. (x - a)(x - b) and multiply up.

I don't see why a GCSE exam question won't ask a student to factorise a quadratic. Yes that's another method that can be used.
Original post by Sir Cumference
I don't see why a GCSE exam question won't ask a student to factorise a quadratic. Yes that's another method that can be used.

Not one with coefficient like that.
Reply 13
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Notnek
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Original post by Muttley79
Not one with coefficient like that.

E.g 2018 OCR Paper 4 question 16:

https://www.ocr.org.uk/Images/528854-question-paper-paper-4.pdf
The X method
Original post by Obolinda
We do use the quadratic formula (that's the calculator method) but paper 1 is non calculator so we need to be able to factorise(not just solve) without.


You can still use the formula without a calculator. The sort of questions that would occur on a non-calculator isn't going to produce surds, you just need proficiency at arithemetic and reasonable knowledge at recognizing perfect squares.
Original post by ghostwalker
You can still use the formula without a calculator. The sort of questions that would occur on a non-calculator isn't going to produce surds, you just need proficiency at arithemetic and reasonable knowledge at recognizing perfect squares.

I guess, yes. :dontknow: I find the quadratic formula way of factorising hard quadratics confusing personally tho

Oh and some non-calculator questions may produce surds but the question asks you to solve by completing the square
I used to use the ‘common’ AC method at gcse, but found it too time consuming when I got to A level. Then I started using the calculator/cheat method, and using the quadratic formula if I didn’t have a calculator (which probably takes even longer).
I can usually do it by inspection now, which I used to find too difficult. I learnt to do it when factorising cubics and quartics.
Original post by Sir Cumference

3 is prime which makes a huge difference - your example did not have that; hence my comment
Reply 19
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Notnek
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Original post by Muttley79
3 is prime which makes a huge difference - your example did not have that; hence my comment

Ok change the example in my post to 3x2+11x−203x^2+11x-20 and the thread and subsequent posts still apply. But it's important to note that the DFE content says that students need to "factorise quadratics of the form ax2+bx+cax^2+bx+c" and doesn't say anything about aa being prime only. It would be very risky for students to assume that nothing as hard as the question in my OP will come up in the Higher papers.

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