What is important to know about Quadratic equations (factorising)?

Rearrange to ax² + bx + c = 0 before factorising.

What is important to know about Quadratic equations (factorising)?

Factorise into two brackets, then set each bracket = 0.

What is important to know about Quadratic equations (factorising)?

A quadratic can have 0, 1 or 2 solutions.

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Algebra · Higher

Quadratic equations (factorising)

Quadratic equations have the form ax² + bx + c = 0. When the quadratic can be factorised, you set each bracket to zero to find the solutions (roots).

Revising quadratic equations (factorising) the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Quadratic equations (factorising) GCSE” on the site for the complete guide.

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Key facts to remember

1Rearrange to ax² + bx + c = 0 before factorising.
2Factorise into two brackets, then set each bracket = 0.
3A quadratic can have 0, 1 or 2 solutions.
4If the equation is x² = k, then x = ±√k.
5For ax² + bx + c where a ≠ 1, find factors of ac that sum to b.

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Worked examples

Example 1

Solve x² + x − 6 = 0

Working

Find factors of −6 that sum to +1: +3 and −2
(x + 3)(x − 2) = 0
x + 3 = 0 → x = −3
x − 2 = 0 → x = 2

Answerx = −3 or x = 2

Example 2

Solve 2x² + 5x − 3 = 0

Working

a × c = 2 × (−3) = −6
Find factors of −6 that sum to 5: +6 and −1
2x² + 6x − x − 3 = 0
2x(x + 3) − 1(x + 3) = 0
(2x − 1)(x + 3) = 0
x = 1/2 or x = −3

Answerx = 1/2 or x = −3

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Common mistakes

✗Not rearranging to = 0 first (e.g. trying to factorise x² + x = 6).

✗Only giving one solution — quadratics almost always have two.

✗Setting ax² = 0 to get x = 0 instead of factorising properly.

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Exam tips

✓Always rearrange so one side is zero before factorising.

✓Check your solutions by substituting both back into the original equation.

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