14 May 2014

Factorising Harder Quadratics

My pupils panic at the sight of a quadratic with a leading coefficient greater than one.  I factorise these quadratics by inspection (the 'guess and test' method) but my pupils aren't satisfied with this suggestion - they want a more structured approach.

A commonly taught method in the UK involves splitting the middle term in two (sometimes called the 'Grouping Method'). This is explained very clearly here (thanks to SRWhitehouse for this resource). Teachitmaths.co.uk has a PowerPoint explaining this method. It's worth watching James Tanton's video 'Splitting the Middle Term' too. He's not a fan!
'Grouping'. Source: Flat World Education
An alternative, which seems easy at first but paves the way for a large number of misconceptions, is the 'slide and divide' method. The method, and its associated problems, are nicely described in Nix the Tricks.
Nix the Tricks offers an interesting alternative - I've provided two examples here but it's worth reading the book for the full explanation.
It's also worth looking at this post by Don Steward to see his tap top method for finding factors and for lots of helpful practice questions.
Also worth a mention: when I first start teaching quadratic factorisation, I like to use this well-designed sum-product worksheet from greatmathsteachingideas.com as a starter. It's good practice of an essential skill.


  1. Hi Jo! I've posted my favourite way on Twitter here:

    Links in with the grid method which we use regularly, including for dividing polynomials at A-level.

  2. Here's a recording of a 25 Feb 2014 Global Mathematics Department presentation which covers the topic of "monic trinomials", starting around the half-way mark:


  3. My attempt to describe and illustrate the process of quadratic factorisation is in this post http://www.thewessens.net/blog/2015/06/22/cracking-the-quadratic-code/. I wanted to show that the splitting method is essentially the same thing as students are already comfortable doing with monic quadratics.

  4. I always use the quadratic formula. You only need to learn one procedure and it always works. Why don't students and teachers in the UK use the quadratic formula more often?

    1. Factorising is more efficient. I'd always rather factorise if I can.

    2. Drawing the distinction between finding roots aka solution and factorising must be emphasised. Can students see the link between factorising and solving? I love the FORMULA but I will keep Quadratic formula for later until they draw that link. Also introducing formula too quick disconnect the sense of students relating or seeing quadratic expressions on a grid re graphs.

  5. In GCSE exams, students are sometimes specifically asked to factorise so are required to understand and use this technique. In addition it is often very efficient and can be used with expressions not just equations (handy for proofs).