Factorising General Quadratics
Any expression of the form
cannot 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
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 of
by the constant term:
Find the two factors of this product which add to give the coefficient of
which 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 of
by the constant term:F
ind 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 form
can be factorised almost instantly:
Example:
Example:
