2. Quadratic expressions with 2 terms
x2 – 3x
Is there anything common?
Yes
Take it out
x(x – 3) No
Is it difference of two squares?
x2 - 9
(x – 3)(x +3)

3. Examples to work out
4x2 – xy
x(4x- y)
12y + 8y2
4y(3 + 2y)

4. Quadratic expressions with 3 terms
x2 + 7x + 10
Look at the last sign
+ means the brackets will both have the same sign
It also means that the numbers are added to make 7
Look at the first sign
+ means the brackets will be both +
Think of two numbers which when multiplied give you 10 and added give you 7
(x + 5)(x +2)

5. Practice
x2 + 6x + 5
(x + 5)(x + 1)
x2 - 10x + 21
(x – 7)(x – 3)

6. x2 + 3x -10
Look at the last sign
- means the brackets will have a different sign
It also means that the numbers are minused to make 3
Look at the first sign
+ means that the larger number will be positive
Think of two numbers which when multiplied give you 10 and minused give you 3
(x + 5)(x -2)

7. Practice
x2 - 10x -24
(x -12)(x + 2)
x2 + x - 12
(x + 4)(x-3)

8. Paper A factorisation
In paper 2A expressions might have a coefficient of x2
This means that it will have a number in front of it.
2x2 + 11x + 12
In this case the factors of 2x2 and of 12 must be opened to find the values
(2x + 3)( x +4)
6x2 - 11x + 3
(2x - 3)( 3x -1)

9. Practice
4x2 - 16x + 15
(2x - 3)( 2x -5)
5x2 +23x -10
(5x - 2)( x +5)