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In this video we’re going to discover how to factorise quadratics. Quadratics are expressions with x² as the highest power. Expanding and factorising are opposites. Factorising means to put into brackets, and with quadratics it is usually 2 brackets (x + 2)(x - 3). Each bracket is a factor. Let's factorise x² + 3x - 10. Start by putting down your two brackets, both with an ‘x’ at the front: (x )(x ). Now look at the number that is on it's own at the end: -10. What multiplies to give negative 10? 2 and 5, or 1 and 10. Which combination of those add to give the number in the middle: + 3? +5, -2. So put these into the brackets. (x + 5)(x - 2). And that is the quadratic factorised. It is really important to check yourself, so quickly expand your answer to double check you’ve factorised correctly. Quadratics that start as x-squared, so with no number in front of the x² are called monic quadratics. Quadratics that have a coefficient in front of the x-squared, like 3x2 are called non-monic quadratics. They are a little harder to factorise.
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