# Which method do you use to factorise hard quadratics?

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Announcements Poll: Which method do you use?
Inspection / trial and error (6)
40%
The "common" AC method (0)
0%
The "alternative" AC method (0)
0%
The perfect square method (1)
6.67%
The calculator/cheat method (5)
33.33%
Something else (specify in the comments) (3)
20%
#1
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. 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 -------------------------------------------------------------------------------------------------------------------------------------------------

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

Methods

Inspection/trial and error : Try factors of the first and last terms inside the brackets until you end up with the correct answer. This method requires lots of practice.

The "common" AC method : Start by multiplying the 'a' and 'c' so in the case above it would give 36 then look for two numbers that add to give 13 and multiply to give 36. They are 4 and 9 so split the middle term to give . Then factorise by grouping to give .

The "alternative" AC method : Start the same as above but then put the numbers you found straight into the brackets with 'ax' at the front of both e.g. . Then "cancel"/divide one or both of the brackets, here you do both to give .

The perfect square method : Start by multiplying/dividing by 'a' so e.g. changes into and then factorise the easier quadratic .

The calculator/cheat method : Use your calculator to solve the equation which gives and . Then use your knowledge of quadratic equations to work backwards and end up with . Of course this can't be used in GCSE Paper 1!
0
11 months ago
#2

Or is that not GCSE?
Last edited by ghostwalker; 11 months ago
1
11 months ago
#3
I find inspection works best for me, but the a-levels calculator has given me the luxury of it doing everything for me We only ever got taught the inspection/trial and error method in school so I find the AC methods really interesting!
1
11 months ago
#4
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
0
#5
(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.
0
11 months ago
#6
(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
0
11 months ago
#7
Don't think mine is listed First I have to choose the 2 number that make 4x^2 !!!
0
11 months ago
#8
(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.
1
#9
(Original post by Obolinda)
Don't think mine is listed First I have to choose the 2 number that make 4x^2 !!!
That's the inspection/trial and error method I mentioned 1
11 months ago
#10
(Original post by Sir Cumference)
That's the inspection/trial and error method I mentioned Oh (Original post by ghostwalker)

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.
0
11 months ago
#11
(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 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!
0
#12
(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.
0
11 months ago
#13
(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.
0
#14
(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...er-paper-4.pdf
0
11 months ago
#15
The X method
0
11 months ago
#16
(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.
0
11 months ago
#17
(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. 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
1
11 months ago
#18
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.
2
11 months ago
#19
(Original post by Sir Cumference)
E.g 2018 OCR Paper 4 question 16:

https://www.ocr.org.uk/Images/528854...er-paper-4.pdf
3 is prime which makes a huge difference - your example did not have that; hence my comment
0
#20
(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 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 " and doesn't say anything about 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.
0
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