Skip to main content
MathidiaMathematics Academy
Quadratic equations and graphs
Lesson 16 of 75
Introduction

Solve quadratics by factorising

Objective. Find roots by expressing a quadratic as a product of factors.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Solving a quadratic by factorising uses the fact that if two factors multiply to give zero, at least one of them must equal zero. First rearrange the equation so one side is zero, then factorise the quadratic expression into two brackets, and finally set each bracket equal to zero to find the two possible values of x. For example, x² − 5x + 6 = 0 factorises to (x − 2)(x − 3) = 0, giving x = 2 or x = 3. Always check the equation equals zero before factorising, as the zero-product rule only applies then.

Worked example

Solve the quadratic equation x² + 2x − 15 = 0 by factorising, giving both solutions.

2 … 15
Illustrated card showing 2 … 15
  1. 1Find two numbers multiplying to −15 and summing to 2: 5 and −3.
  2. 2Factorise: (x + 5)(x − 3) = 0.
  3. 3Set each bracket to zero: x + 5 = 0 or x − 3 = 0.
  4. 4Solve each: x = −5 or x = 3.

Answer: x = −5 or x = 3

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Pupils factorise a quadratic correctly but then set the brackets equal to the original constant instead of zero, such as solving (x − 2)(x − 3) = 6 by writing x − 2 = 6. Always rearrange to equal zero first.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard