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Chapter 5: Problem 3

Factorise (a) \(x^{2}+x\), (b) \(3 x^{2}+6 x\) (c) \(9 x^{2}-12 x\).

Short Answer

Expert verified
Answer: The factorised forms are: (a) \(x(x+1)\), (b) \(3x(x+2)\), and (c) \(3x(3x-4)\).

Step by step solution

01

Identify the common factors of terms.

Look for the factors that are common to all the terms in the given expression.
02

Factor out the common factors.

Take the common factors outside the parenthesis and write the remaining expression inside. (a) \(x^{2}+x\)
03

Identify the common factors of terms.

The common factor for both terms is 'x'.
04

Factor out the common factors.

We take 'x' as a common factor from both terms and put the remaining expression in parenthesis: \(x(x+1)\) So, the factorised form of \(x^{2}+x\) is \(x(x+1)\). (b) \(3x^{2}+6x\)
05

Identify the common factors of terms.

The common factors for both terms are '3' and 'x'.
06

Factor out the common factors.

We take '3x' as a common factor from both terms and put the remaining expression in parenthesis: \(3x(x+2)\) So, the factorised form of \(3x^{2}+6x\) is \(3x(x+2)\). (c) \(9x^{2}-12x\)
07

Identify the common factors of terms.

The common factors for both terms are '3' and 'x'.
08

Factor out the common factors.

We take '3x' as a common factor from both terms and put the remaining expression in parenthesis: \(3x(3x-4)\) So, the factorised form of \(9x^{2}-12x\) is \(3x(3x-4)\).

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