Factorize the following
$11 + 5 x - 6 x^{2}$

(x + 1) (11 - 6 x)

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(x - 1) (11 - 6 x)

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(x + 1) (11 + 6 x)

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None of these

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Solution

The correct option is A $(x + 1) (11 - 6 x)$
Given,
$11 + 5 x - 6 x^{2}$

$- 11 + 6 = - 5$ ..........the split for the middle term

$- 11 \times 6 = - 66$ .............the product of the coefficient of the first and last term
Now splitting the middle term, we get

$= - (6 x^{2} - 5 x - 11)$

$= - (6 x^{2} + 6 x - 11 x - 11)$
$= - (6 x (x + 1) - 11 (x + 11))$

$= - (6 x - 11) (x + 1)$

$= (11 - 6 x) (x + 1)$

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The value of the integral $\int (x^{2} + x) (x^{- 8} + 2 x^{- 9})^{1 / 10} d x$ is

|\begin{matrix} x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x \end{matrix}|

|\begin{matrix} x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x \end{matrix}|

x + \frac{1}{x} = 11 \frac{1}{11}

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