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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 Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX

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