One of the factors of $x^{2} - 2 x - 15$ is _____.

x+3

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x-3

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x+5

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x - 15

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Solution

The correct option is A
x+3

The given expression is

$x^{2} - 2 x - 15$

We have to split the middle term in such a way the sum is -2 and product is -15 , which can be done in following way

$= x^{2} - 5 x + 3 x - 15 = x (x - 5) + 3 (x - 5)$
$= (x + 3) (x - 5)$

So, $x + 3$ is one of the factors of the given expression.

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