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:  2x2 + 4x = 2x(x + 2)

2. Difference of Squares

a² - b² = (a - b)(a + b)

Example: x2 - 9 = (x - 3)(x + 3)

3. Trinomials (ax² + bx + c)

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

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

Example: x2 + 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.