§ 1. When it is necessary to find the factors of such an expression as x2 – 7x – 120 the difficulty for beginners lies in finding the pair of factors of 120 which satisfy the middle term: in this case so that their difference is 7. They may write down the pairs in order (1 × 120; 2 × 60; etc.) and then choose the suitable pair, but this method is often long; or they may guess until they chance to find the pair required. This is often done in so haphazard a fashion that much time is wasted, especially if the given expression have no rational factors.