Factorise the following. x 2 + a + 1 a x + 1

We need to factorise the expression x 2 + a + 1 a x + 1 . x 2 + a + 1 a x + 1 = x 2 + a x + x a + 1 Taking out the common factors, we get: x 2 + a x + x a + 1 = x ( x + a ) + 1 a ( x + a ) = ( x + a ) x + 1 a Hence, the given expression can be factorised and expressed as ( x + a ) x + 1 a .

Factorise the following. 2 x 2 - 3 x - 3

Given trinomial is 2 x 2 - 3 x - 3 . To factorise the above trinomial we have to find two integers whose sum is - 3 and product is 2 × - 3 = - 6 . We have, - 2 3 + 3 = - 3 and - 2 3 × 3 = - 2 × 3 = - 6 . ∴ 2 x 2 - 3 x - 3 = 2 x 2 - 2 3 x + 3 x - 3 = 2 x ( x - 3 ) + 3 ( x - 3 ) = ( x - 3 ) ( 2 x + 3 ) Hence, the given expression can be factorised as ( x - 3 ) ( 2 x + 3 ) .

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ICSE Understanding Mathematics Class 8>Chapter 11 - Factorisation>Higher Order Thinking Skills(HOTS)

M L Aggarwal Solutions for Chapter: Factorisation, Exercise 3: Higher Order Thinking Skills(HOTS)

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Factorisation, Exercise 3: Higher Order Thinking Skills(HOTS)

Attempt the practice questions on Chapter 11: Factorisation, Exercise 3: Higher Order Thinking Skills(HOTS) with hints and solutions to strengthen your understanding. ICSE Understanding Mathematics Class 8 solutions are prepared by Experienced Embibe Experts.