Basic Factorising
What is factorisation?
- A factorised expression is one written as the product (multiplication) of two, or more, terms (factors)
- 3(x + 2) is factorised
- It is 3 × (x + 2)
- 3x + 6 is not factorised
- 3xy is factorised
- It is 3 × x × y
- Numbers can also be factorised
- 12 = 2 x 2 x 3
- 3(x + 2) is factorised
- In algebra, factorisation is the reverse of expanding brackets
- It's putting it into brackets, rather than removing brackets
How do I factorise two terms?
- To factorise 12x2 + 18x
- Find the highest common factor of the number parts
- 6
- Find the highest common factor of the algebra parts
- x
- Multiply both to get the overall highest common factor
- 6x
- 12x2 + 18x is the same as 6x × 2x + 6x × 3
- Using the highest common factor
- Take out the highest common factor
- Write it outside a set of brackets
- Put the remaining terms, 2x + 3, inside the brackets
- This gives the answer
- 6x (2x + 3)
- Find the highest common factor of the number parts
- To factorise an expression containing multiple variables, e.g. 2a3b - 4a2b2
- Use the same approach as above
- Find the highest common factor of the number parts
- 2
- Find the highest common factor of the algebra parts
- a and b appear in both terms
- The highest common factor of a3 and a2 is a2
- The highest common factor of b and b2 is b
- a2b
- Multiply both to get the overall highest common factor
- 2a2b
- 2a3b - 4a2b2 is the same as 2a2b × a - 2a2b × 2b
- Using the highest common factor
- Take out the highest common factor
- Write it outside a set of brackets
- Put the remaining terms, a - 2b, inside the brackets
- This gives the answer
- 2a2b (a - 2b)
Examiner Tip
- In the exam, check that your factorisation is correct by expanding the brackets!
- Factorise mean factorise fully.
- x (6x + 10) is not fully factorised but 2x (3x + 5) is.
Worked example
Factorise 5x + 15
Find the highest common factor of 5 and 15
5
There is no x in the second term, so no highest common factor in x is needed
Think of each term as 5 × something
5 × x + 5 × 3
Take out the 5 and put x + 3 in brackets
5(x + 3)
5(x + 3)
Think of each term as 6x × something
6x × 5x - 6x × 4
Take out the 6x and put 5x - 4 in brackets
6x (5x - 4)
6x (5x - 4)