Factorize the following
$x^{2} - 14 x + 24$

(x - 2) (x - 12)

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(x + 2) (x - 12)

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(x - 2) (x + 12)

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None of these

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Solution

The correct option is A $(x - 2) (x - 12)$
In the given polynomial $x^{2} - 14 x + 24$ ,

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

The middle term is $- 14 x$ and its coefficient is $- 14$ .

The last term is a constant term $24$ .

Multiply the coefficient of the first term by the constant $1 \times 24 = 24$ .

We now find the factor of $24$ whose sum equals the coefficient of the middle term, which is $- 14$ and then factorize the polynomial $x^{2} - 14 x + 24$ as shown below:
$x^{2} - 14 x + 24$

$= x^{2} - 12 x - 2 x + 24$

$= x (x - 12) - 2 (x - 12)$

$= (x - 2) (x - 12)$

Hence, $x^{2} - 14 x + 24 = (x - 2) (x - 12)$ .

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