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Chapter 12: Factorisation

    Introduction

    Factors of Algebraic Expressions

    Need of Factorisation

    Method of Common Factors

    Factorisation by grouping the terms

    Factorisation using Identities

    Factors of the form (x+a)(x+b) = x² + (a+b)x + ab

    Division of Algebraic Expressions

    Division of a Monomial by another Monomial

    Division of an Expression by a Monomial

    Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial)

    Exercise 12.1

    Exercise 12.2

    Exercise 12.3

    Exercise 12.4

    What We Have Discussed?

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 12: Factorisation > Division of a Monomial by another Monomial

Division of a Monomial by another Monomial

Division of a monomial by another monomial

Take for example the division: 6x3÷2x

Like earlier we will write each of the involved terms in irreducible factor forms:

2x = 2 × x

6x3=2×3×x×x×x

Now we take a look at what are the common factors amongst them which cancel each other:

6x3 = 2 × x × (3 × x × x) = (2x) × (3x2)

Now,

Instructions

6x3÷2x

  • Between the numerator and denominator, cancel out the common factors
  • We get:
  • We cancel out 2 and x
  • Which gives the above answer

Thus, the answer for the division, 6x3 ÷ 2x is 3x2.

Example 13: Do the following divisions.

Instructions

(i) −20x4 ÷ 10x2
−20x4 = × × × × × × while 10x2 = × × ×
−20x4 ÷ 10x2 = −2×2×5×x×x×x×x2×5×x×x = × × =
(ii) 7x2y2z2 ÷ 14xyz
7x2y2z2 = × × × × × × while 14xyz = × × × ×
7x2y2z2 ÷ 14xyz = 7×x×x×y×y×z×z2×7×x×y×z =