Question

Which among the given options is one of the factors of
$x^2+\frac{x}{6}-\frac{1}{6}$?

• A. $3x+1$
• B. $2x+1$
• C. $x-\frac{1}{5}$
• D. $x-\frac{1}{2}$

Answer 1

The correct option is B $2x+1$

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

Now, we will factorise the above polynomial.
$\frac{1}{6}(6x^2+x-1)$

The middle term has to split in such a way that sum or difference is 1 and product of coefficient is -6.

$=\frac{1}{6}(6x^2+3x-2x-1)$
$=\frac{1}{6}\left[3x\right(2x+1)-1(2x+1\left)\right]$
$=\frac{1}{6}(3x-1)(2x+1)$

$\therefore$The factors of $x^2+\frac{x}{6}-\frac{1}{6}$ are
$\frac{1}{6},(3x-1)and(2x+1).$