A comprehensive guide and pitfalls to avoid

The general procedure for factoring

When faced with an expression to factor, follow this procedure:

1. Count the number of terms (separated by + or -)
2. Look for a common factor shared by all the terms: a number, a letter, or an expression in brackets
3. Bring this common factor out in front of a set of brackets
4. Check your result by expanding it again: you should get the original expression back

Step-by-step example

Factorise D = 4x(x+1) - 6(x+1).

• Two terms, each containing (x+1)
• Common factor: (x+1)
• What remains after factoring: 4x and -6
• D = (x+1)(4x-6)
• We can continue, as 4x – 6 = 2(2x – 3), so D = 2(x + 1)(2x – 3)

Summary table of common mistakes

Common mistake	Why it’s wrong	Correct approach
Stopping at a common factor that is too small	The result is not fully factored	Look for the largest common factor
Forgetting the minus sign in front of a term	Changes the final result	Copy out each sign carefully
Not checking your answer	An error may go unnoticed	Always work it out again to check

Common pitfall

The most important pitfall to bear in mind: a factored expression is a PRODUCT (of factors multiplied together), never a sum. If your final result still contains a + or – sign outside any multiplied brackets, it is not fully factored.