A factor is a number that will go into another without leaving a remainder. Factorising means looking for a common factor, which can be a letter, a number or both, and taking it outside the brackets.

Example 1
3x + 6
3(x + 2)
The common factor is 3.

Example 2
x² – 2x
x(x – 2)
The common factor is x.

Example 3
2x² – 4x
2x(x – 2)
The common factor is 2x

When factorising always check that when you multiply out the brackets in your answer you get back to the expression you started with. If this does not work you have gone wrong!

Factorise these expressions.
HINT Don't put any spaces in your answer.
Make sure the answer is fully factorised. eg

5xy+10xyz = 5(xy+2xyz) = 5x(y+2yz) =5xy(1+2z)
Only the last answer is fully factorised.

1. 4x – 12 = 4()

2. 25p + 5= (5p+1)

3. 8a + 4 = (2a +1)

4. ab + a = a()

5. 3x + 12y=

6. 120x + 6 =

7. 4a + 12b =

8. 3x + 6y + 12z =

9. 10 – 5y=

10. 12p – 3q =

11. 5x² + 4x=

12. 3y – 6y² =

13. 4b² + b=

14. 3z - z²=

15. p² – 2p =

16. n - n²=

17. m² + 2m=

18. a³ + a = (a²+1)

19. 2x³ + 3x= (2x² + 3)

20. 4y⁴ +3y³= y³()

21. 6x² + 3x=

22. 4y² – 8y=

23. 5x – 15x² =

24. 9b² + 3b =

25. 4xy³ + 12y= (xy² + 3)

26. 6p – 9p³ = (2-3p²)

27. a²b + ab=

28. 3p²q + 2pq =