If 2 divides $x^{2} + 6 x + 9$ then x + 3 would be a/an for any value of x, provided $x^{2} + 6 x + 9$ is a positive integer.

prime number

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odd number

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even number

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Solution

The correct option is C even number
2 divides $x^{2} + 6 x + 9 = (x + 3)^{2}$
$\Rightarrow 2$ divides $x + 3$ ( $∵$ For any prime number p and a positive integer b, if $p$ divides $b^{2}$ , then $p$ divides $b$ )
$\Rightarrow x + 3$ is even $(∵$ Numbers divisible by 2 are even)

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\dots

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