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Understanding the X factor

Q I am a student support assistant and have been doing a lot of work in mathematics. I have started an AS-level in mathematics, but I am having some problems in factorising expressions. The problem is that my teacher and other people in my class seem to pluck the correct values out of the air, but I can't see where they get them from; this is even harder when there is a number in front of x2. For example, the answer to factorising 2x2 + 3x - 2 is (2x - 1) (x + 2). I know that this is right as I can multiply out the brackets and get the quadratic, but I can't get the brackets from the quadratic. Can you help me?

A The problem stems, I think, from the approach taken when teaching the multiplying out of the brackets. The approach I prefer is the following as it then translates to helping in the understanding of factorising quadratic expressions.

The example I shall use is (2x - 1) (x + 2). Write this as 2x (x + 2) - 1(x + 2) this is an important stage giving 2x2 + 4x - x - 2 = 2x2 + 3x - 2.

Now I will describe how this can be factorised easily:

Wendy Fortescue-Hubbard is a teacher, game inventor and member of the London Mathematical Society. She has been awarded a three-year fellowship by the National endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses. Email your questions to Mathagony Aunt at teacher@tes.co.uk Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX

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