STEP 1 Question: A Step-by-step guide

Show that

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can be written as

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when Q(x) is a quadratic expression. Show that 2Q(x) can be written as the sum of three expressions, each of which is a perfect square.

This is just the first part from Question 4 of the STEP1 2007 paper. It quickly becomes clear if one tries to use long division that (x+b+c) doesn’t provide a clean, easy division. The STEP instructions explain that the fastest route in answering the questions is always by inspection.

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Welcome back (It’s matt again)

From now I endeavor to create an actually active blog. I’ll probably keep it appropriate to the work I’m doing at the moment – my A-Levels. I hope to keep to some academic updates of my Politics, Physics, Chemistry and Mathematics over the next two years (and it may be of use to anyone also interested or studying those courses)