Factorising

• Factorising involves rewriting an algebraic expression as a product of its factors. Factors are expressions which divide exactly into the original expression.
• Simple factorising often refers to taking out a common factor from each term in the expression. For example, factorising 3x + 9y would result in 3(x + 3y).
• When factorising quadratics of the form x^2 + bx + c, look for two numbers that add to equal b and multiply to equal c. These will form the brackets of your factorised expression.
• The difference of squares is a special type of quadratic often encountered while factorising. Understand that a^2 - b^2 can be factored into (a-b)(a+b).
• Higher degree polynomials can be factored by grouping terms together and factoring out common terms. This process may need to be repeated until the expression can no longer be factored.
• The method of “completing the square” can be used to factorise quadratic expressions, and is particularly useful when the quadratic is not easily factorisable by other means. It involves rearranging the quadratic into the form (x+a)^2 + b.
• Recognise and understand the factor theorem, which states that for a polynomial, if f(a) = 0, then (x-a) is a factor of f(x).
• Sometimes it may not be possible to factorise an expression cleanly with integer values. In this case, the quadratic formula may be used to find the solutions, which might be irrational or complex numbers.
• Practice both guiding factorising problems and also work on spotting opportunities to factorise in broader algebraic problems, as it can often simplify complex expressions and make solving equations easier.
• Knowledge of other Algebra topics, such as simplifying, expanding and solving equations, will be useful in aiding factorisation.