Question

Factors of (x²+x/6-1/6) are

Answer 1

Hey friend
Ur Ans!


X^2 +X/6 -1/6
Take LCM

=> 1/6 * (6x^2 +X -1)

=> 1/6 * (6x^2 +3x -2x -1)

=> 1/6 * {3x(2x +1) -1(2x+1)}

=> 1/6 * (3x-1) ( 2x+1)

So correct option B)

Hope it's helpful ✌☺

Answer 2

Given:

$\mathbf{x^{2}+\dfrac{x}{6}-\dfrac{1}{6}}$

To Find:

What are factor of given equation ?

Solution:

Come to equation:

$\mathbf{x^{2}+\dfrac{x}{6}-\dfrac{1}{6}}$

Here L.C.M of denominator is 6:

$\mathbf{\dfrac{6x^{2}+x-1}{6}}$

Numerator can factorize by middle term splitting method:

$\mathbf{\dfrac{6x^{2}+3x-2x-1}{6}}$

Taking common 3x in first and second term. Taking common -1 in third and fourth term of numerator:

$\mathbf{\dfrac{3x(2x+1)-1(2x+1)}{6}}$

$\mathbf{\dfrac{(3x-1)(2x+1)}{6}}$

Above factorization can be written as :

$\mathbf{\dfrac{1}{6}\times (2x+1)\times (3x-1)}$

Means its factor are (2 x +1) , (3 x -1) and  $\mathbf{\dfrac{1}{6}}$ . Option second is correct.