Factorise 2*x^2 - 4*x - 6

The question asks us to factorise the quadratic 2x^2 - 4x - 6. All quadratics are of the form ax^2 + bx + c, so we have a = 2, b = -4, c = 6. I would advise approaching it using the product and sum approach. Firstly, we need to find two numbers with the following properties: their product equals ac, which here is 2(-6) = -12, and their sum equals b, which here is -4. The only ways to get -12 are: 4*(-3), 3*(-4), 12*(-1), 1*(-12), 2*(-6) and 6*(-2). We can easily see that the only pair with a sum of -4 are 2 and -6 (since 2 - 6 = -4). We then rewrite our quadratic, but split our ‘x’ term into two separate ‘x’ terms (so split -4x into 2x – 6x). So 2x^2 - 4x - 6 = 2x^2 + 2x - 6x - 6. We then factorise the first two terms together, which is easy since we just find the common factors of 2x^2 and 2x (which is just 2x) and multiply this by a bracket that multiplies out to 2x^2 + 2x, giving us 2x (x + 1). We copy this approach for the last two terms (-6x - 6), so our overall quadratic is now 2x^2 + 2x - 6x - 6 = 2x (x + 1) - 6(x + 1). Using this method, we have that the bracket used is always the same (the (x+1) appears twice). So we can use the idea of adding like terms together, with (x+1) as the like term, and its coefficient being (2x - 6). Now, in our quadratic equation, we have 2x (x + 1) - 6(x + 1) = (2x - 6)(x+1). This is the final answer to our question! And we can multiply it out using the grid method to see that it equals our original quadratic, to check for any errors we could have made, which is possible under exam pressure!