Factorising Quiz Generator
Make a factorising quiz: taking out a common factor, factorising with x, and factorising quadratics into two brackets, with the factor pairs shown.
- Free
- No sign-up to try
- Works as you type
Preview: 10 questions
1. Factorise fully: 7x + 21
2. Factorise fully: 12x − 30
3. Factorise fully: 5x + 45
4. Factorise fully: 24x + 56
5. Factorise fully: 6x + 8
6. Factorise fully: 9x + 12
7. Factorise fully: 8x + 40
8. Factorise fully: 10x + 14
9. Factorise fully: 10x + 25
10. Factorise fully: 10x − 18
Free, no sign-up to try. Your quiz becomes a Room you can edit, publish and share.
How it works
How the Factorising Quiz Generator works
- 1
Pick skills and difficulty
Choose the skills to practise, how hard, and how many questions.
- 2
Try it here
The quiz appears as you choose. Answer a few and check them to see the worked solutions.
- 3
Create the Room
One click makes it a quiz Room with a tutor that gives hints. Publish it and share the link.
Worked example
What it makes
Three questions from a easier quiz on factorising, with the answers and worked solutions the quiz shows after checking.
1. Factorise fully: 7x + 21
Options: 7(x + 2) · 7(x − 3) · 7(x + 3) · 7(x + 21)
Answer: 7(x + 3)
The highest common factor of 7 and 21 is 7. Divide each term by 7: 7x ÷ 7 = x and 21 ÷ 7 = 3. So 7(x + 3).
2. Factorise fully: 12x − 30
Options: 6(2x + 5) · 6(2x − 5) · 6(2x − 30) · 2(6x − 15)
Answer: 6(2x − 5)
The highest common factor of 12 and 30 is 6. Divide each term by 6: 12x ÷ 6 = 2x and −30 ÷ 6 = −5. So 6(2x − 5).
3. Factorise fully: 5x + 45
Options: 5(x + 9) · 5(x + 8) · 5(x + 45) · 5(x − 9)
Answer: 5(x + 9)
The highest common factor of 5 and 45 is 5. Divide each term by 5: 5x ÷ 5 = x and 45 ÷ 5 = 9. So 5(x + 9).
Who it's for
Who uses it
Maths teachers
Practice that pairs with expanding brackets.
Learners
Learn to look for the highest common factor.
Tutors
Practise finding two numbers that multiply and add to given values.
Good to know
What to consider
- 'Factorise fully' means taking out the highest common factor; a partly factorised option is marked wrong.
- Quadratics have x² on its own (coefficient 1) and two different whole-number roots.
- Levels are difficulty bands, not school grades or a curriculum.
Questions
About the Factorising Quiz Generator
Does it include the difference of two squares?
Sometimes, at level 3: x² − 25 = (x − 5)(x + 5) comes up as one of the quadratics.
How do I know the answers are right?
The questions are computed, not written by AI: each answer is worked out with exact arithmetic and checked again by a separate solver in our tests. Every question shows its worked solution after the learner checks their answers.
Can my students use it without an account?
Yes. Publish the Room and share the link: anyone with it can take the quiz, check their answers and read the worked solutions. You need a free account to keep and publish the Room.
Make your quiz now
Free, no sign-up to try. It becomes a Room you can edit, publish and share.
Create my quizRelated
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