What this covers
Factorising is taught in Year 11 (age 15 to 16, KS4) as a topic to introduce. It sits in the Algebra strand.
Worked example
Factorise fully: x^2 - 5x - 14
- Find two numbers that multiply to -14 and add to -5
- The factor pairs of -14 include (-7, 2), and -7 + 2 = -5
- Write as double brackets: (x - 7)(x + 2)
Answer: (x - 7)(x + 2)
Difficulty scale
The sheet generator offers five difficulty settings for this topic.
- Common numerical factor only, e.g., 6x + 9 = 3(2x + 3)
- Common algebraic and numerical factor, e.g., 4x^2 - 6x = 2x(2x - 3)
- Simple quadratic trinomials x^2 + bx + c with positive terms
- Quadratic trinomials x^2 + bx + c involving negative terms
- Difference of two squares and quadratics with a > 1, e.g., 2x^2 + 7x + 3
Common mistakes
- Partially factorising by taking out only a numerical factor when a variable is also common
- Confusing signs when factorising quadratics with a negative constant term
Curriculum links
Indicative matches to National Curriculum for England. Check wording and codes against the official document.
- Factorise quadratic expressions including the difference of two squares and trinomials.