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Prerequisites

- A1a – Using and interpreting algebraic notation
- A2a – Substituting numerical values into formulae and expressions
- A4a – Simplifying and manipulating algebraic expressions by collecting like terms (basic)
- A4b – Multiplying a single term over a bracket
- A4c – Factorising (basic)
- A4d – Multiplying two or more brackets

# Factorising quadratics

Click the tabs for extension tasks…

- Fully factorise \(x^4-1\)

- Define \(u = x^2\). Then \(u^2=x^4\).

- \(x^4-1 \equiv u^2-1 \equiv (u+1)(u-1) \equiv (x^2+1)(x^2-1) \equiv (x^2+1)(x+1)(x-1)\)

- Expand \((x+\frac{1}{2})(x+6)\). Is it possible factorise this expanded expression so that the factors only contain integer coefficients and constants?
- Expand \((x+\frac{1}{2})(2x+6)\). Is it possible factorise this expanded expression so that the factors only contain integer coefficients and constants?

- \((x+\frac{1}{2})(x+6)\equiv x^2+\frac{13}{2}x+3\); no
- \((x+\frac{1}{2})(2x+6)\equiv 2x^2+7x+3 \equiv (2x+1)(x+3)\)

Stan and Ollie are trying to factorise \(x^2-5x+6\). Stan writes \((x-2)(x-3)\). Ollie writes \((2-x)(3-x)\). Are either of them correct? If so, who?

Hover for answers:

- They’re both correct, but Stan’s factorisation is more conventional.

Teacher resources

Links to past exam and UKMT questions

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Unlimited practice questions

In the real world

In lesson A18a, you will see how factorising quadratic expressions will help you solve quadratic equations. The ‘

*In the real world*‘ section for that lesson shows why quadratics are so relevant in the real world.