Factorising by common factors and grouping: Class 8 practice
Factorising is the reverse of expanding. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- HCF
- Expanding brackets
The idea behind factorising by common factors and grouping
Factorising is the reverse of expanding. First take out the highest common factor of every term; with four terms, group them in pairs that share a factor.
Step-by-step method
- Find the HCF of all terms and take it out.
- With four terms, pair them so each pair has a common factor.
- Take out the common bracket.
- Expand to check.
Worked example 1 (Basic)
Factorise 28x + 35.
- HCF of the terms = 7
- = 7(4x + 5)
- Answer: 7(4x + 5)
Worked example 2 (Standard)
Factorise 8x² + 4x.
- HCF of the terms = 4x
- = 4x(2x + 1)
- Answer: 4x(2x + 1)
Worked example 3 (Challenge)
Factorise x² + 2x + 2x + 4.
- x(x + 2) + 2(x + 2)
- = (x + 2)(x + 2)
- Answer: (x + 2)(x + 2)
Common mistakes and misconceptions
- Taking out a factor from only some terms
- Losing a sign when grouping
Practice questions
- (Basic) Factorise 16x + 28.
- (Basic) Factorise 18x + 16.
- (Standard) Factorise 49x² + 7x.
- (Standard) Factorise 54x² + 99x.
- (Challenge) Factorise x² + 6x + 4x + 24.
- (Challenge) Factorise x² + 5x + 5x + 25.
Answer key with full working
- Q1: HCF of the terms = 4 → = 4(4x + 7) → Answer: 4(4x + 7)
- Q2: HCF of the terms = 2 → = 2(9x + 8) → Answer: 2(9x + 8)
- Q3: HCF of the terms = 7x → = 7x(7x + 1) → Answer: 7x(7x + 1)
- Q4: HCF of the terms = 9x → = 9x(6x + 11) → Answer: 9x(6x + 11)
- Q5: x(x + 6) + 4(x + 6) → = (x + 6)(x + 4) → Answer: (x + 6)(x + 4)
- Q6: x(x + 5) + 5(x + 5) → = (x + 5)(x + 5) → Answer: (x + 5)(x + 5)
Syllabus note
This skill is listed under "Factorisation" for Class 8 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is factorising by common factors and grouping in?
"Factorisation", Class 8 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.