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Year 10
Factorising
Definition
Factorising rewrites an expression as things multiplied together, the reverse of expanding brackets. x² − 5x + 6 becomes (x − 2)(x − 3), which reveals the values that make it zero.
Why Do I Have to Learn This?
Factorising breaks expressions into their building blocks. It makes hard algebra simpler and reveals hidden solutions.
Key Rules:
- 1. Take out the highest common factor first: 6x + 9 = 3(2x + 3).
- 2. For x² + bx + c, find two numbers that multiply to c and add to b.
- 3. Check by expanding the brackets back out.
Remember:
- •Common slip: sign errors, in (x − 2)(x − 3) the numbers multiply to +6 but add to −5.
- •A difference of two squares has its own shortcut: x² − 9 = (x + 3)(x − 3).
- •Factorised form shows the roots: each bracket equal to zero gives a solution.
Common factor
A factor that two or more numbers share.
1, 2, 3 and 6 are common factors of 12 and 18.
Animated Example:
y = 1x²
Free Factorising Worksheet
Download free worksheets and practise today.
Every download has a fresh set of questions.
Let’s Practise the Concept
Step 1 of 3
Put them in order
Tap the numbers from smallest to largest.
In order so far: nothing yet