## 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: