Factorising Quadratics
Factorising quadratics reverses the expansion process. Given a quadratic expression like x^2 + bx + c, we find two binomials that multiply to give it, a key skill for solving quadratic equations.
What You Need to Know
Key Concept Diagram
To factorise x^2 + bx + c, find two numbers that add to b and multiply to c
x^2 + bx + c = (x + p)(x + q) where p + q = b and p x q = c
Difference of two squares: a^2 - b^2 = (a + b)(a - b)
Always check your factorisation by expanding back out
Key Vocabulary
Quadratic
An expression or equation where the highest power of the variable is 2
Factor
A number or expression that divides exactly into another
Difference of two squares
The pattern a^2 - b^2 = (a+b)(a-b)
Zero product property
If (a)(b) = 0, then a = 0 or b = 0
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Factorise: x^2 + 7x + 12
Question 2
Factorise: x^2 - 25
Question 3
Factorise: x^2 - 5x + 6
Key Concepts Summary
- ●To factorise x^2 + bx + c, find two numbers that add to b and multiply to c
- ●x^2 + bx + c = (x + p)(x + q) where p + q = b and p x q = c
- ●Difference of two squares: a^2 - b^2 = (a + b)(a - b)
- ●Always check your factorisation by expanding back out