07Emixedfactorising

= Mixed Factorising =

When faced with any factorising question, consider the following (in order) :


 * Common Factor **
 * ALWAYS look for a common factor first.
 * Take out the common factor and consider the expression inside the brackets using the following list.


 * Two Terms **
 * 1) Is it a difference of two squares? (** a² – b² **) Use the difference of two squares rule.


 * Three Terms **
 * 1) Is it a quadratic? (** ax² + bx + c **)
 * 2) Is ** a = 1 **?
 * 3) Can you find factors of ** c ** that add or subtract to give ** b **? Use the shortcut.
 * 4) Otherwise, use completing the square.
 * 5) (** a ≠ 1 **)
 * 6) Can you find factors of ** a × c ** that add or subtract to give ** b **? Use the full method.
 * 7) Otherwise, take out a as a common factor and use completing the square


 * Four Terms **
 * 1) Can you factorise by grouping 2 and 2? Factorise and then look for a common bracket.
 * 2) Otherwise, can you factorise by grouping 3 and 1? Factorise and then look for a difference of two squares.


 * Fully Factorised **

An expression is ** fully factorised ** when it is either
 * in the form a(b + c) ... ... ... ... {where ** (b + c) ** is as simple as possible}
 * in the form a(b + c)(d + e) ... .. {where ** (b + c) ** and ** (d + e) ** are as simple as possible}