Factorise: x + 1 x + 2 - a + 1 a 2

Given, x + 1 x + 2 - a + 1 a 2 = x 2 + 2 + 1 x + 1 × 2 - a a 2 - 1 a 2 = x 2 + 3 x + 2 - 1 a - 1 a 2 = x 2 + 2 x + x a + x + 2 + 1 a - x a - 2 a - 1 a 2 = x x + 2 + 1 a + 1 x + 2 + 1 a - 1 a x + 2 + 1 a = x + 2 + 1 a x + 1 - 1 a Therefore, x + 1 x + 2 - a + 1 a 2 = x + 2 + 1 a x + 1 - 1 a

Factorise: x - 1 x - 5 - 2 a + 1 a 2

Given, x - 1 x - 5 - 2 a + 1 a 2 = x 2 + - 1 + - 5 x + - 1 × - 5 - 2 a a 2 - 1 a 2 = x 2 - 6 x + 5 - 2 a - 1 a 2 = x 2 + x a - 3 x - x a - 1 a 2 + 3 a - 5 x - 5 a + 15 = x x + 1 a - 3 - 1 a x + 1 a - 3 - 5 x + 1 a - 3 = x + 1 a - 3 x - 1 a - 5 Therefore, x - 1 x - 5 - 2 a + 1 a 2 = x + 1 a - 3 x - 1 a - 5

Factorise: x + 5 x + 9 + 127 32 2

Given, x + 5 x + 9 + 127 32 2 = x 2 + 5 + 9 x + 5 × 9 + 127 32 2 = x 2 + 14 x + 45 + 127 32 2 = x 2 + 14 x + 45 × 1024 + 127 1024 = x 2 + 14 x + 45 × 1024 + 127 1024 = x 2 + 14 x + 46207 1024 = x 2 + 287 32 x + 161 32 x + 46207 1024 = x x + 287 32 + 161 32 x + 287 32 = x + 287 32 x + 161 32 Therefore, x + 5 x + 9 + 127 32 2 = x + 287 32 x + 161 32

Factorize: 3 - 1 x 2 - 2 x - 3 + 1

Given: 3 - 1 x 2 - 2 x - 3 + 1 . Here we need to split the middle term. We know that: 2 = 3 + 1 - 3 - 1 ⇒ 3 - 1 x 2 - 3 + 1 - 3 - 1 x - 3 + 1 ⇒ 3 - 1 x 2 + 3 - 1 x - 3 + 1 x - 3 + 1 ⇒ 3 - 1 x x + 1 - 3 + 1 x + 1 ⇒ 3 - 1 x - 3 + 1 x + 1 ∴ 3 - 1 x 2 - 2 x - 3 + 1 = 3 - 1 x - 3 + 1 x + 1 .

Factorize: 2 - 1 x 2 + 2 2 x + 2 + 1

Given: 2 - 1 x 2 + 2 2 x + 2 + 1 . Here we need to split the middle term. We know that: 2 2 = 2 - 1 + 2 + 1 ⇒ 2 - 1 x 2 + 2 - 1 + 2 + 1 x + 2 + 1 ⇒ 2 - 1 x 2 + 2 - 1 x + 2 + 1 x + 2 + 1 ⇒ 2 - 1 x x + 1 + 2 + 1 x + 1 ⇒ 2 - 1 x + 2 + 1 x + 1 ∴ 2 - 1 x 2 + 2 2 x + 2 + 1 = 2 - 1 x + 2 + 1 x + 1 .

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MATHEMATICS CLASS 9>Algebra>Chapter 4 - Factorisation>EXERCISE-2.2

Kesab Chandra Nag Solutions for Exercise 3: EXERCISE-2.2

Author:Kesab Chandra Nag

Kesab Chandra Nag Mathematics Solutions for Exercise - Kesab Chandra Nag Solutions for Exercise 3: EXERCISE-2.2

Attempt the practice questions from Exercise 3: EXERCISE-2.2 with hints and solutions to strengthen your understanding. MATHEMATICS CLASS 9 solutions are prepared by Experienced Embibe Experts.