Factorise 7x^2+4x-3

look for common factors but there are not any in this case, it is a quadratic with 3 terms therefore it can be factorised into 2 brackets. First we look at the first term, since 7 is a prime number you can only have (7x.....)(x.....). next you must find 2 numbers that multiply to give the last term -3 (also a prime number therefore can either be -1 and 3 or 1 and -3). so you have a couple of possibilities: (7x + 1)(x -3), (7x -1)(x+3) etc... you must find the combination that also satisfies the fact that once expanded the coefficient of the x term is 4, therefore the correct answer is (7x - 3)(x + 1)