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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 Algebraic Expressions Continued (Polynomial ÷ Polynomial)

Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial)

When we a polynomial in both the numerator and the denominator, we factorise them both and bring them down to their irreducible forms and accordingly check for any common factors(like earlier).

Solve 7x2+14x÷x+2

Instructions

Factorise7x2+14x

  • Factorised form of numerator:
  • Now, 7x2+14x÷x+2 =
  • Thus, the quotient is 7x after cancelling the common factor: (x+2)

Example 15: Divide 44x4−5x3−24x2 by 11xx−8

Instructions

We have: 44x4−5x3−24x2 = × × ×
= 2 × 2 × 11 ×
= 2 × 2 × 11 × x2[x (x – 8) + 3(x – 8)] = 2 × 2 × 11 × x2
44x4−5x3−24x2 ÷ 11xx−8 = 2×2×11×x2x+3x−811×x×x−8
= × × =

Example 16: Divide z5z2−80 by 5zz+4

Instructions

Simplifying: z5z2−80 = z((5 × z2) – (5 × ))
= z×5×z2−16 = 5z ×
z5z2−80 ÷ 5zz+4 = 5z×z+4z−45zz+4 =
Now, let's move on to the exercises.