Factorising Quadratics

Let's look at an example: x² + 6x + 8 = 0.
We can rewrite it as x² + 2x + 4x + 8 = 0.

We can factorise this into two terms: x (x + 2) + 4 (x + 2) = 0.
Notice that (x + 2) appears twice: it is a common factor!

We can factorise the expression further to: (x + 4)(x + 2) = 0
giveing the correct solutions: x=-4 and x=-2.

You may have spotted that 4 + 2 = 6 and that 4 × 2 = 8.

Similar quadratic equations can be factorised and solved if the number on its own (c in the standard equation) has factors that add up to b (the number of x's).

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