Question

factors of (x²+x/6-1/6)

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Answer 1

       $\underline{\bold{Answer:}}$

       $(2x+1) \text{ and }(3x-1)$

       $\underline{\bold{Step-by-step-explaination:}}$

       $\text{The given equation is }x^{2} + \dfrac{x}{6} - \dfrac16 = 0$

       $\text{Multiplying by 6 on both sides}$

$\implies 6(x^{2} + \dfrac{x}6 - \dfrac16) = 0$

       $\text{Simplifying...}$

$\implies 6x^{2} + x - 1 = 0$

       $\text{We can split }x \text{ as }(3x-2x)$

$\implies 6x^{2} + 3x - 2x - 1 = 0$

       $\text{Simplifying...}$

$\implies 3x(2x + 1)-1( 2x + 1) = 0$

       $\text{Taking }(2x+1) \text{ common}$

$\implies (2x+1)(3x-1) = 0$

 $\therefore \text{ }\text{ The factors of the equation }x^{2} + \dfrac{x}{6} - \dfrac16 = 0 \text{ are }(2x+1) \text{ and }(3x-1)$