Factorising quadratics

Factorising where

It is possible to factorise a quadratic expression, such as , into a factorised form*, such as .

For a simple quadratic where (the coefficient of ) is , we find two numbers which multiply to give , and add to give . In this case: and .

Example: factorise

• We need two numbers which multiply to give , and add to give .
• The numbers and work, since and .
• Therefore, we can factorise as .

Factorising where

When is not equal to , we can use a method called splitting the middle term (or simply called ‘the split method’).

First, we multiply and together. Then, we find two numbers which multiply to give , and add to give . We then split the middle term using these two numbers, and factor by grouping.

Example: factorise

• , and .
• .
• We need two numbers which multiply to give , and add to give
• The numbers and work, since and .
• Split the middle term into and :
• Use the distributive law to factor by grouping:
• Factor out the common factor :
• Answer: .

Example: factorise

• , and .
• .
• We need two numbers which multiply to give , and add to give $-11
• The numbers and work, since and .
• Split the middle term into and :
• Use the distributive law to factor by grouping:
• Factor out the common factor :
• Answer: .

Solving quadratic equations by factorising

Please see solving-quadratics-by-factorising.