Quadratic Equations by Factorisation

Secondary School Maths

Example 1

Factorise x² + 8x + 15

To factorise quadratis, look for two numbers such that when you add them you will get 8, which is the coefficient of x; and when you multiply them you will get 15.

Therefore, we will have (x + 3)(x + 5)

Example 2

Solve the equation x² + 8x + 15 = 0

(x + 3)(x + 5) = 0

x + 3 = 0

x = -3

and

x + 5 = 0

x = -5

Try the questions below from Edexcel GCSE Exam Papers, UK:

Factorise x² + 6x + 8
1. (x + 6)(x + 8)
2. (x + 2)(x + 4)
3. (x - 2)(x - 4)
4. (x + 2)(x + 6)
Factorise x – 7x + 12
1. (x - 3)(x - 4)
2. (x + 3)(x + 4)
3. (x + 7)(x + 5)
4. (x - 12)(x - 7)
Factorise x² – 3x – 18
1. (x - 9)(x + 2)
2. (x - 18)(x - 3)
3. (x - 6)(x + 3)
4. (x - 6)(x + 3)
Factorise x² – 4x – 45
1. (x + 4)(x - 5)
2. (x - 5)(x + 9)
3. (x + 5)(x - 9)
4. (x + 9)(x - 4)
Factorise x² – x – 56
1. (x + 7)(x - 8)
2. (x + 56)(x - 1)
3. (x - 7)(x + 8)
4. (x + 4)(x - 14)