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Factorisation

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Method of Common Factors

Subtopic

Method of Common Factors under Factorisation for Grade 8 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Factorise: 21a2−14a21a^2 - 14a

    A.

    7a(3a−2)7a(3a - 2)

    B.

    7(3a2−2a)7(3a^2 - 2a)

    C.

    a(21a−14)a(21a - 14)

    D.

    7a(3a−14)7a(3a - 14)

  2. 2.

    Factorise the expression: 16x2y2−8xy16x^2y^2 - 8xy

    A.

    8xy(2xy−1)8xy(2xy - 1)

    B.

    8xy(2xy−8)8xy(2xy - 8)

    C.

    4xy(4xy−2)4xy(4xy - 2)

    D.

    8x2y2(1−1/2xy)8x^2y^2(1 - 1/2xy)

  3. 3.

    Factorise: 9m2−12m9m^2 - 12m

    A.

    3m(3m−4)3m(3m - 4)

    B.

    3(3m2−4m)3(3m^2 - 4m)

    C.

    m(9m−12)m(9m - 12)

    D.

    3m(3m−12)3m(3m - 12)

Download the worksheet for Factorisation - Method of Common Factors to practice offline. It includes additional chapter-level practice questions.

Factorisation by Regrouping Terms

Subtopic

Factorisation by Regrouping Terms under Factorisation for Grade 8 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Factorise: x2+x−2x−2x^2 + x - 2x - 2

    A.

    (x+1)(x−2)(x+1)(x-2)

    B.

    (x−1)(x+2)(x-1)(x+2)

    C.

    (x+1)(x+2)(x+1)(x+2)

    D.

    (x−1)(x−2)(x-1)(x-2)

  2. 2.

    What is the factorised form of 12a2+4a+3ab+b12a^2 + 4a + 3ab + b?

    A.

    (4a+b)(3a+1)(4a+b)(3a+1)

    B.

    (4a+1)(3a+b)(4a+1)(3a+b)

    C.

    (3a+1)(4a−b)(3a+1)(4a-b)

    D.

    (12a+b)(a+1)(12a+b)(a+1)

  3. 3.

    Factorise: x2−xy+7x−7yx^2 - xy + 7x - 7y

    A.

    (x−y)(x+7)(x-y)(x+7)

    B.

    (x+y)(x−7)(x+y)(x-7)

    C.

    (x−y)(x−7)(x-y)(x-7)

    D.

    (x+y)(x+7)(x+y)(x+7)

Download the worksheet for Factorisation - Factorisation by Regrouping Terms to practice offline. It includes additional chapter-level practice questions.

Factorisation using Identities

Subtopic

Factorisation using Identities under Factorisation for Grade 8 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Factorise 64b2−48b+964b^2 - 48b + 9.

    A.

    (8b+3)2(8b+3)^2

    B.

    (8b−3)(8b+3)(8b-3)(8b+3)

    C.

    (8b−3)2(8b-3)^2

    D.

    (64b−9)2(64b-9)^2

  2. 2.

    Factorise the quadratic expression 81a2+18a+181a^2 + 18a + 1.

    A.

    (9a−1)2(9a-1)^2

    B.

    (9a+1)2(9a+1)^2

    C.

    (9a+1)(9a−1)(9a+1)(9a-1)

    D.

    (81a+1)2(81a+1)^2

  3. 3.

    Factorise 49−x249 - x^2.

    A.

    (7−x)(7+x)(7-x)(7+x)

    B.

    (7−x)2(7-x)^2

    C.

    (x−7)(x+7)(x-7)(x+7)

    D.

    (7+x)2(7+x)^2

Download the worksheet for Factorisation - Factorisation using Identities to practice offline. It includes additional chapter-level practice questions.

Factorisation of the form (x+a)(x+b)

Subtopic

Factorisation of the form (x+a)(x+b) under Factorisation for Grade 8 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Identify the factors of x2−3x−18x^2 - 3x - 18.

    A.

    (x+6)(x−3)(x+6)(x-3)

    B.

    (x−6)(x+3)(x-6)(x+3)

    C.

    (x−9)(x+2)(x-9)(x+2)

    D.

    (x−6)(x−3)(x-6)(x-3)

  2. 2.

    Factorise: x2−2x−15x^2 - 2x - 15.

    A.

    (x−5)(x+3)(x-5)(x+3)

    B.

    (x+5)(x−3)(x+5)(x-3)

    C.

    (x−15)(x+1)(x-15)(x+1)

    D.

    (x−3)(x−5)(x-3)(x-5)

  3. 3.

    What are the factors of x2−x−12x^2 - x - 12?

    A.

    (x+4)(x−3)(x+4)(x-3)

    B.

    (x−6)(x+2)(x-6)(x+2)

    C.

    (x+3)(x−4)(x+3)(x-4)

    D.

    (x−4)(x+3)(x-4)(x+3)

Download the worksheet for Factorisation - Factorisation of the form (x+a)(x+b) to practice offline. It includes additional chapter-level practice questions.

Division of Polynomials

Subtopic

Division of Polynomials under Factorisation for Grade 8 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Divide (x2−10x+25)(x^2 - 10x + 25) by (x−5)(x - 5).

    A.

    x+5x + 5

    B.

    x−10x - 10

    C.

    55

    D.

    x−5x - 5

  2. 2.

    What is the result of dividing 30x2y230x^2y^2 by 6xy6xy?

    A.

    5x2y25x^2y^2

    B.

    24xy24xy

    C.

    5xy5xy

    D.

    5x3y35x^3y^3

  3. 3.

    Find the quotient: (4x2+4x+1)÷(2x+1)(4x^2 + 4x + 1) \div (2x + 1).

    A.

    2x+12x + 1

    B.

    2x−12x - 1

    C.

    x+1x + 1

    D.

    4x+14x + 1

Download the worksheet for Factorisation - Division of Polynomials to practice offline. It includes additional chapter-level practice questions.