Free Grade 3 Introducing Factorising Quadratics Worksheets
Free Grade 3 worksheets for Introducing 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
Core
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing factorising quadratics
Explain introducing factorising quadratics accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing factorising quadratics
Calculate introducing factorising quadratics accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing factorising quadratics
Compare introducing factorising quadratics accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing factorising quadratics
Justify introducing 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 Introducing 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 + 3x − 40.[1]
- 2.Factorise x² + 4x − 45.[1]
- 3.Factorise x² − 1x − 6.[1]
- 4.Factorise x² + 14x + 49.[1]
- 5.Solve x² + 1x − 2 = 0.[2]
- 6.Solve x² + 6x − 27 = 0.[2]
- 7.Solve x² + 4x − 21 = 0.[2]
- 8.Solve x² − 2x − 3 = 0.[2]
- 9.Solve x² + 0x − 4 = 0.[3]
- 10.Solve x² + 4x + 4 = 0.[3]
- 11.Solve x² + 8x − 9 = 0.[3]
- 12.Solve x² + 1x − 6 = 0.[3]
Show answers and working
1. (x − 5)(x + 8)
Find two numbers that multiply to -40 and add to 3: -5 and 8. So x² + 3x − 40 = (x − 5)(x + 8).
2. (x − 5)(x + 9)
Find two numbers that multiply to -45 and add to 4: -5 and 9. So x² + 4x − 45 = (x − 5)(x + 9).
3. (x + 2)(x − 3)
Find two numbers that multiply to -6 and add to -1: 2 and -3. So x² − 1x − 6 = (x + 2)(x − 3).
4. (x + 7)(x + 7)
Find two numbers that multiply to 49 and add to 14: 7 and 7. So x² + 14x + 49 = (x + 7)(x + 7).
5. x = -2 or x = 1
Factorise: (x + 2)(x − 1) = 0. One bracket must be zero: x = -2 or x = 1.
6. x = 3 or x = -9
Factorise: (x − 3)(x + 9) = 0. One bracket must be zero: x = 3 or x = -9.
7. x = -7 or x = 3
Factorise: (x + 7)(x − 3) = 0. One bracket must be zero: x = -7 or x = 3.
8. x = -1 or x = 3
Factorise: (x + 1)(x − 3) = 0. One bracket must be zero: x = -1 or x = 3.
9. x = -2 or x = 2
Factorise: (x + 2)(x − 2) = 0. One bracket must be zero: x = -2 or x = 2.
10. x = -2 or x = -2
Factorise: (x + 2)(x + 2) = 0. One bracket must be zero: x = -2 or x = -2.
11. x = 1 or x = -9
Factorise: (x − 1)(x + 9) = 0. One bracket must be zero: x = 1 or x = -9.
12. x = -3 or x = 2
Factorise: (x + 3)(x − 2) = 0. One bracket must be zero: x = -3 or x = 2.
Worked examples
Factorise x² + 5x + 6.
- Find two numbers that multiply to 6 and add to 5: 2 and 3.
- So x² + 5x + 6 = (x + 2)(x + 3).
- Answer: (x + 2)(x + 3)
Solve x² − 2x − 48 = 0.
- Factorise: (x + 6)(x − 8) = 0.
- One bracket must be zero: x = -6 or x = 8.
- Answer: x = -6 or x = 8
Solve x² + 14x + 48 = 0.
- Factorise: (x + 8)(x + 6) = 0.
- One bracket must be zero: x = -8 or x = -6.
- Answer: x = -8 or x = -6
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
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Frequently asked
- Is this Grade 3 Introducing Factorising Quadratics worksheet really free?
- Yes. Every worksheets 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. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 Introducing Factorising Quadratics?
- Move on to Working with Factorising Quadratics, Factorising Quadratics in Context, Expanding Double Brackets, Completing the Square, which build directly on this idea.
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