Welcome to factorising harder quadratics. You've likely already met quadratics like x-squared plus 5x plus 6. The quadratics in this deck are a step up, because the x-squared term has a coefficient, or number in front of it, that is greater than 1. For example, 2x-squared plus 7x plus 3.

These expressions are in the general form 'a x-squared plus b x plus c'. The letter 'a' stands for the coefficient of the x-squared term, 'b' is the coefficient of the x term, and 'c' is the constant term at the end.

Factorising these harder quadratics requires a reliable method. The most common one is often called the 'ac method', because it starts by multiplying the numbers 'a' and 'c' together. Let's walk through it with the example 2x-squared plus 7x plus 3.

In our example, 2x-squared plus 7x plus 3, 'a' is 2 and 'c' is 3. So, the product 'ac' is 2 times 3, which equals 6. The next step is to find two numbers that multiply to give this value, 6, but add to give the middle coefficient, 'b', which is 7.