Factorise x^2 -7x+10, and hence solve x^2-7x+10=0

Firstly, it is important to recognise that the answer will need to be in the form of two pairs of brackets because the question is asking us to factorise a quadratic equation. The equation only has a single x^2, so there will be one x within each pair of brackets. Next, note that the sign before the end term is a +, so the signs in both of the brackets are the same. In order to determine which sign this is, look at the middle term of the equation; it is -7, so both of the brackets will have a - sign in the bracket. At this stage we know the answer will look like (x - _)(x - _), with _ representing a missing number which we need to work out.In order to work out the missing numbers, we again need to look at the middle and end terms of the equation. The numbers must multiply to give the end term, and add to give the middle term. In this example, the numbers must multiple to give 10, and add to give 7; therefore the missing numbers are 5 and 2. This then allows us to complete the first part of the question with the answer (x - 5)(x - 2). To answer the second part of the question, simply put (x-5)(x-2) = 0 and solve each bracket for x. This gives the two answers x = 5 and x = 2.