Free Grade 3 Factorising Quadratics Lessons
Free Grade 3 lessons for Factorising Quadratics: 12 real questions with a full answer key and worked solutions. A quadratic has an x² term. Factorise by finding two numbers that multiply to the constant and add to the x-coefficient; each bracket gives a solution.
Free
Foundation
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify factorising quadratics
Identify factorising quadratics accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain factorising quadratics
Explain factorising quadratics accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate factorising quadratics
Calculate factorising quadratics accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare factorising quadratics
Compare factorising quadratics accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Factorising Quadratics works
A quadratic has an x² term. Factorise by finding two numbers that multiply to the constant and add to the x-coefficient; each bracket gives a solution.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Factorise x² + 9x + 14.[1]
- 2.Factorise x² − 3x − 10.[1]
- 3.Factorise x² − 10x + 21.[1]
- 4.Factorise x² + 16x + 63.[1]
- 5.Solve x² − 5x − 36 = 0.[2]
- 6.Solve x² − 1x − 6 = 0.[2]
- 7.Solve x² + 12x + 35 = 0.[2]
- 8.Solve x² + 6x + 5 = 0.[2]
- 9.Solve x² + 1x − 20 = 0.[3]
- 10.Solve x² − 9x + 20 = 0.[3]
- 11.Solve x² + 10x + 25 = 0.[3]
- 12.Solve x² − 2x − 63 = 0.[3]
Show answers and working
1. (x + 2)(x + 7)
Find two numbers that multiply to 14 and add to 9: 2 and 7. So x² + 9x + 14 = (x + 2)(x + 7).
2. (x + 2)(x − 5)
Find two numbers that multiply to -10 and add to -3: 2 and -5. So x² − 3x − 10 = (x + 2)(x − 5).
3. (x − 3)(x − 7)
Find two numbers that multiply to 21 and add to -10: -3 and -7. So x² − 10x + 21 = (x − 3)(x − 7).
4. (x + 9)(x + 7)
Find two numbers that multiply to 63 and add to 16: 9 and 7. So x² + 16x + 63 = (x + 9)(x + 7).
5. x = -4 or x = 9
Factorise: (x + 4)(x − 9) = 0. One bracket must be zero: x = -4 or x = 9.
6. x = -2 or x = 3
Factorise: (x + 2)(x − 3) = 0. One bracket must be zero: x = -2 or x = 3.
7. x = -5 or x = -7
Factorise: (x + 5)(x + 7) = 0. One bracket must be zero: x = -5 or x = -7.
8. x = -5 or x = -1
Factorise: (x + 5)(x + 1) = 0. One bracket must be zero: x = -5 or x = -1.
9. x = 4 or x = -5
Factorise: (x − 4)(x + 5) = 0. One bracket must be zero: x = 4 or x = -5.
10. x = 4 or x = 5
Factorise: (x − 4)(x − 5) = 0. One bracket must be zero: x = 4 or x = 5.
11. x = -5 or x = -5
Factorise: (x + 5)(x + 5) = 0. One bracket must be zero: x = -5 or x = -5.
12. x = -7 or x = 9
Factorise: (x + 7)(x − 9) = 0. One bracket must be zero: x = -7 or x = 9.
Worked examples
Factorise x² + 11x + 18.
- Find two numbers that multiply to 18 and add to 11: 2 and 9.
- So x² + 11x + 18 = (x + 2)(x + 9).
- Answer: (x + 2)(x + 9)
Solve x² + 6x − 7 = 0.
- Factorise: (x + 7)(x − 1) = 0.
- One bracket must be zero: x = -7 or x = 1.
- Answer: x = -7 or x = 1
Solve x² − 1x − 72 = 0.
- Factorise: (x − 9)(x + 8) = 0.
- One bracket must be zero: x = 9 or x = -8.
- Answer: x = 9 or x = -8
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Gives x = 3 from (x + 3) = 0.
Correction: x + 3 = 0 means x = −3.
Gets the signs muddled when factorising.
Correction: Check by expanding the brackets.
Teacher tips
- · Use a product–sum grid for finding the pair.
Parent tips
- · Ask what two numbers multiply to 12 and add to 7.
Real-life applications
- · Projectile paths, maximising area.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Factorising Quadratics lesson really free?
- Yes. Every lessons on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Expanding Double Brackets, Sequences. Each one has its own free lesson, worksheet and quiz.
- How is the lesson sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Factorising Quadratics?
- Move on to Completing the Square, The Quadratic Formula, Quadratic Graphs, Algebraic Expressions, which build directly on this idea.
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