Factorising General Quadratics
Any expression of the formcannot be factorised as with simple quadratics, by finding factors of c. Instead there is a slightly more complicated procedure, best illustrated by an example:
Factorise

Take out any common factor. Every term in the above expression has a factor 3, so we may write the expression as

Multiply the coefficient ofby the constant term:Find the two factors of this product which add to give the coefficient ofwhich in this case is 1.

Rewrite the term in brackets using these two factors:

Take out common factors for each pair:

Factorise completely:
Example
Factorise

Take out common factors:

Multiply the coefficient ofby the constant term:Find the two factors of this product which add to give the coefficient ofwhich in this case is 7: 1 and 6.

Rewrite the term in brackets using these two factors:

Take out common factors for each pair:

Factorise completely:
Differences of Squares
Any expression of the formcan be factorised almost instantly:
Example:
Example: