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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-18-GRP-01
Common Factors & Grouping - Assignment
Chapter: Factorisation
Topic: Factorisation by Common Factors and Grouping
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The first step in factorisation is to take out the:
  • A.largest term
  • B.common factor (HCF)
  • C.constant
  • D.square
2.
$6x+9=$
  • A.$3(2x+3)$
  • B.$3(2x+9)$
  • C.$6(x+3)$
  • D.$3(x+3)$
3.
$x^2+x=$
  • A.$x(x+1)$
  • B.$x^2(1+x)$
  • C.$(x+1)^2$
  • D.$x(1-x)$
4.
$ax+bx=$
  • A.$x(a+b)$
  • B.$ab(x)$
  • C.$x(ab)$
  • D.$a+bx$
5.
Grouping is usually used with ___ terms.
  • A.two
  • B.three
  • C.four
  • D.one
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Factorise $4x+8$.
7.
Factorise $5x^2-10x$.
8.
Factorise $ax+ay$.
9.
Factorise $3a^2b+6ab^2$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Factorise $x^2+xy+x+y$.
11.
Factorise $6xy+4y+9x+6$.
12.
Factorise $ab-a-b+1$.
13.
Factorise $2x^3-4x^2+x-2$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Factorise completely: $12a^2b-18ab^2+24ab$.
15.
Factorise by grouping: $x^3+x^2+x+1$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) common factor (HCF)
  2. (A) $3(2x+3)$
  3. (A) $x(x+1)$
  4. (A) $x(a+b)$
  5. (C) four
Section B — Short Answer (2 marks)
  1. $4(x+2)$.
  2. $5x(x-2)$.
  3. $a(x+y)$.
  4. $3ab(a+2b)$.
Section C — Short Answer (3 marks)
  1. $(x+1)(x+y)$.
  2. $(3x+2)(2y+3)$.
  3. $(a-1)(b-1)$.
  4. $(x-2)(2x^2+1)$.
Section D — Long Answer (5 marks)
  1. $6ab(2a-3b+4)$.
  2. $(x+1)(x^2+1)$.
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