Factorise-103 x-1 x 2-3 x-1 x-3

Given: 10(3x+1/x)^2 (3x+1/x) 3Replace 3x+1/x=a,⇒ 10a^2 a 3⇒ 10a^2 6a+5a 3 nbsp; [Using Middle Term Splitting]⇒ 2a(5a 3)+1(5a 3)⇒ (2a+1)(5a 3)⇒ (2(3x+1/x)+1) ...

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Standard IX

Mathematics

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Factorise:103...

Question

Factorise: $10 (3 x + \frac{1}{x})^{2} - (3 x + \frac{1}{x}) - 3$

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Solution

Given: $10 (3 x + \frac{1}{x})^{2} - (3 x + \frac{1}{x}) - 3$
Replace $3 x + \frac{1}{x} = a$ ,
$\Rightarrow 10 a^{2} - a - 3$
$\Rightarrow 10 a^{2} - 6 a + 5 a - 3$ [Using Middle Term Splitting]
$\Rightarrow 2 a (5 a - 3) + 1 (5 a - 3)$
$\Rightarrow (2 a + 1) (5 a - 3)$
$\Rightarrow (2 (3 x + \frac{1}{x}) + 1) (5 (3 x + \frac{1}{x}) - 3)$
$\Rightarrow (6 x + \frac{2}{x} + 1) (15 x + \frac{5}{x} - 3)$
Hence, $10 (3 x + \frac{1}{x})^{2} - (3 x + \frac{1}{x}) - 3 = (6 x + \frac{2}{x} + 1) (15 x + \frac{5}{x} - 3)$

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Factorise: 10(3x+1x)2−(3x+1x)−3

Given: 10(3x+1x)2−(3x+1x)−3Replace 3x+1x=a,⇒10a2−a−3⇒10a2−6a+5a−3 [Using Middle Term Splitting]⇒2a(5a−3)+1(5a−3)⇒(2a+1)(5a−3)⇒(2(3x+1x)+1)(5(3x+1x)−3)⇒(6x+2x+1)(15x+5x−3)Hence, 10(3x+1x)2−(3x+1x)−3=(6x+2x+1)(15x+5x−3)

Factorise: $10 (3 x + \frac{1}{x})^{2} - (3 x + \frac{1}{x}) - 3$