Year 10: Factorising polynomials

Factorising polynomials means breaking them down into simpler expressions by finding the factors. Here’s a cheat sheet to help you.

Key concepts

• Factors: Numbers or expressions that, when multiplied together, result in a given polynomial.
• Factorising: Finding the factors of a polynomial.

Common methods

1. Common factor method

Find the greatest common factor (GCF) of all terms and factor it out.

Example:  $2x^2+4x=2x(x+2)$

2. Difference of squares

$a^2-b^2=(a-b)(a+b)$

Example: $x^2-9=(x-3)(x+3)$

3. Trinomials $(a{x}^2+bx+c)$

Method 1: Trial and Error (guess factors of 'ac')

Method 2: Factorisation by Grouping (useful for more complex trinomials)

Example: $x^2+5x+6=(x+2)(x+3)$

Important notes

• Always check your answer by expanding the factors back to the original polynomial.
• Practice is key! Work through plenty of examples.