STEP 1 Question: A Step-by-step guide

Show that


can be written as


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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Being a British 15 year old, I have a lot of gcse exams over the next few weeks. (I’ve had a few recently already, but they were easy…)

Starting with my literature and sciences next week, and maths, history etc later on.

Either way, good luck to anyone else with exams, and I hope we do well 😀


(picture courtesy of pusheen)