Lucy
Ask the AI Tutor
Need help with Level 7-8 Algebra - Factorisation? Ask our AI Tutor!
Lucy AI Tutor - Lucy
Connecting with Tutor...
Please wait while we establish connection
Lucy
Hi! I'm Lucy, your AI tutor. How can I help you with Level 7-8 Algebra - Factorisation today?
now
0/50 words
  1. Home
  2. KS3
  3. Maths
  4. Level 7-8 Algebra - Factorisation
Logo

Maths Quiz - Level 7-8 Algebra - Factorisation (Questions)

Factorising expressions makes algebra simpler. Spot common factors, take out brackets, and rewrite terms to solve KS3 problems faster and with fewer mistakes.

Fascinating Fact:

Factorisation is also used in physics for simplifying formulas such as force = mass × acceleration, where common terms can cancel.

In KS3 Maths, factorisation helps you rewrite algebraic expressions efficiently. You’ll extract common factors, factorise single brackets (like ax + ay = a(x + y)), and simplify expressions to make equations easier to solve.

Key Terms

  • Factor: A quantity multiplied by another to make a product (e.g., 3 and 4 are factors of 12).
  • Common factor: A number or term that divides every term in an expression.
  • Factorisation: Rewriting an expression as a product, often by taking out the highest common factor.

Frequently Asked Questions (Click to see answers)

What does factorising mean in KS3 algebra?

Factorising means writing an expression as a product. For example, 8x + 12 becomes 4(2x + 3) after taking out the highest common factor 4.

How do I factorise a simple expression like 6x + 9?

Find the highest common factor of 6x and 9, which is 3. Divide each term by 3 to get 3(2x + 3).

What is the difference between expanding and factorising?

Expanding removes brackets (e.g., 3(x + 2) → 3x + 6). Factorising adds brackets by reversing that process (e.g., 3x + 6 → 3(x + 2)).

Try These Related Quizzes

1. What is the common factor in the terms 3x - 9?
[ ] x
[ ] 3
[ ] 6
[ ] 9
2. What is the correct answer when you factorise 3x - 9?
[ ] 3(x - 3)
[ ] 3(x + 3)
[ ] x(3 - 3)
[ ] x(3 + 3)
3. What is the common factor in the terms x2 -5x?
[ ] 2
[ ] 5
[ ] -5
[ ] x
4. What is the correct answer when you factorise x2 -5x?
[ ] x(x - 5)
[ ] x(x + 5)
[ ] x(x2 - 5)
[ ] x(x2 + 5)
5. What are the highest common factors in 4x2y3 + 8xy2?
[ ] 2 and x and y2
[ ] 4 and x
[ ] 4 and x and y2
[ ] 4 and y
6. What is the correct answer when you factorise 4x2y3 + 8xy2?
[ ] 4xy2(x + 2)
[ ] 4xy2(xy + 2)
[ ] 4xy2(xy + 4)
[ ] 4xy2(y + 2)
7. Factorise the following expression into a pair of linear brackets x2 + 7x + 6
[ ] (x + 1)(x + 6)
[ ] (x - 1)(x + 6)
[ ] (x + 1)(x - 6)
[ ] (x - 1)(x - 6)
8. Factorise the following expression into a pair of linear brackets x2 - 5x - 6
[ ] (x - 1)(x - 6)
[ ] (x - 1)(x + 6)
[ ] (x + 1)(x - 6)
[ ] (x + 1)(x + 6)
9. Factorise the following expression into a pair of linear brackets x2 + 8x + 12
[ ] (x - 2)(x - 6)
[ ] (x - 2)(x + 6)
[ ] (x + 2)(x - 6)
[ ] (x + 2)(x + 6)
10. Factorise the following expression into a pair of linear brackets x2 - 9x + 8
[ ] (x + 1)(x + 8)
[ ] (x +1)(x - 8)
[ ] (x -1)(x - 8)
[ ] (x -1)(x + 8)

You can find more about this topic by visiting BBC Bitesize - Factorising

© Education Quizzes. Please visit www.educationquizzes.com to subscribe
Logo
Maths Quiz - Level 7-8 Algebra - Factorisation (Answers)
1. What is the common factor in the terms 3x - 9?
[ ] x
[x] 3
[ ] 6
[ ] 9
3 is a part of both 3x and 9
2. What is the correct answer when you factorise 3x - 9?
[x] 3(x - 3)
[ ] 3(x + 3)
[ ] x(3 - 3)
[ ] x(3 + 3)
The common factor is placed outside the brackets
3. What is the common factor in the terms x2 -5x?
[ ] 2
[ ] 5
[ ] -5
[x] x
x is a part of both x2 and 5x
4. What is the correct answer when you factorise x2 -5x?
[x] x(x - 5)
[ ] x(x + 5)
[ ] x(x2 - 5)
[ ] x(x2 + 5)
The common factor is placed outside the brackets
5. What are the highest common factors in 4x2y3 + 8xy2?
[ ] 2 and x and y2
[ ] 4 and x
[x] 4 and x and y2
[ ] 4 and y
4 is the highest common factor of 4 and 8, x is the highest common factor of x and x2 and y2 is the highest common factor of y2 and y3
6. What is the correct answer when you factorise 4x2y3 + 8xy2?
[ ] 4xy2(x + 2)
[x] 4xy2(xy + 2)
[ ] 4xy2(xy + 4)
[ ] 4xy2(y + 2)
Can you see why?
7. Factorise the following expression into a pair of linear brackets x2 + 7x + 6
[x] (x + 1)(x + 6)
[ ] (x - 1)(x + 6)
[ ] (x + 1)(x - 6)
[ ] (x - 1)(x - 6)
To check each of the answers it is necessary to multiply out the brackets. Remember that each term in each bracket is multiplied by each term in the other bracket
8. Factorise the following expression into a pair of linear brackets x2 - 5x - 6
[ ] (x - 1)(x - 6)
[ ] (x - 1)(x + 6)
[x] (x + 1)(x - 6)
[ ] (x + 1)(x + 6)
The more often you factorise, the easier it will get
9. Factorise the following expression into a pair of linear brackets x2 + 8x + 12
[ ] (x - 2)(x - 6)
[ ] (x - 2)(x + 6)
[ ] (x + 2)(x - 6)
[x] (x + 2)(x + 6)
Can you see the pattern?
10. Factorise the following expression into a pair of linear brackets x2 - 9x + 8
[ ] (x + 1)(x + 8)
[ ] (x +1)(x - 8)
[x] (x -1)(x - 8)
[ ] (x -1)(x + 8)
After you have factorised several expressions you will begin to see patterns emerging that enable you to quickly arrive at the correct answer
© Education Quizzes. Please visit www.educationquizzes.com to subscribe