Factorize the following
$x^{2} + 9 x - 22$

(x - 2) (x + 11)

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(x + 2) (x + 11)

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(x - 2) (x - 11)

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None of these

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Solution

The correct option is A $(x - 2) (x + 11)$
In the given polynomial $x^{2} + 9 x - 22$ ,

The first term is $x^{2}$ and its coefficient is $1$ .

The middle term is $9 x$ and its coefficient is $9$ .

The last term is a constant term $- 22$ .

Multiply the coefficient of the first term by the constant $1 \times (- 22) = - 22$ .

We now find the factor of $- 22$ whose sum equals the coefficient of the middle term, which is $9$ and then factorize the polynomial $x^{2} + 9 x - 22$ as shown below:
$x^{2} + 9 x - 22$
$= x^{2} + 11 x - 2 x - 22$

$= x (x + 11) - 2 (x + 11)$

$= (x - 2) (x + 11)$

Hence, $x^{2} + 9 x - 22 = (x - 2) (x + 11)$ .

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