How do I factorise a quadratic expression with coefficient greater than 1 i.e. 2x^2 + x - 6.

In order to factorise this, we will use the S.P.F method. S, stands for sum (2nd term) P, stands for product (3rd term)F, stands for factors (two numbers). The goal is to find 2 factors that not only add to the coefficient of the 2nd term(S), but also multiply together to get the coefficient of the 3rd term(P) multiplied by the coefficient of the 1st term. Therefore S = 1 and P = -12. In this case the two factors are 4 and -3. This is because 4 x -3 = -12 and 4 + (-3) = 1. This satisfies the conditions for SPF. Now we can rewrite our expression as 2x^2 + 4x - 3x - 6 and separate it into 2 sections. 2x^2+4x and -3x - 6. For each section, 'extract' the high common factor. If this is done correctly, it should leave you with two identical brackets and their extracted highest common factor next to them, 2x(x+2) - 3(x+2). Finally combine the terms outside the brackets to form a single bracket, (2x-3). This multiplied by the repeated bracket is the factorised expression for 2x^2 + x - 6, (2x - 3)(x+2).