Factorisation of Quadratic Expressions

When factorising quadratic expressions do you check coefficients first? If the coefficient of x2 and the constant are prime for example you should be able to just write down the factorisation without needing an elaborate method.

Some students have difficulty with the splitting the middle term method; you might like an alternative – try the box method.

For instructions on the method:

Quadratic Factorisation Box method (pdf file)

Working on Quadratic Grids from Underground Mathematics will help you develop and understand the method.

quadratic-grids

Perhaps even simpler is Lyszkowski’s method which avoids the manipulation required by conventional methods.
Lyszkowski's method

Comparing the two methods with an example:
Lyszkowski & box comparison

We could have a look at the general case for the box method :
Box method general

and for Lyszkowski’s method:
Lyszkowski general
Have a look at this series of videos on Factorising Quadratic Expressions from Exam Solutions. You could try the examples given with the various methods presented.

I would be interested to hear student views, which methods do you like?

 

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