Factorising General Quadratics

Any expression of the formcannot always 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

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

2. 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.

3. Rewrite the term in brackets using these two factors:

4. Take out common factors for each pair:

5. Factorise completely:

Example

Factorise

1. Take out common factors:

2. 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.

3. Rewrite the term in brackets using these two factors:

4. Take out common factors for each pair:

5. Factorise completely:

Differences of Squares

Any expression of the formcan be factorised almost instantly:

Example:

Example: