The real factors of $x^{2} + 16$ are __________.

(x^{2} + 2) (x^{2} - 2)

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(x + 4) (x - 4)

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Does not exist

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(x + 2) (x - 2)

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Solution

The correct option is A Does not exist
For an expression to have real factors, the roots of its equation ( $=$ $0$ ) should be real.
Here, $x^{2} + 16$ is the given expression.
For it to have real roots,
Equation : $x^{2} + 16 = 0$ should have real roots.
$\Rightarrow x^{2} = - 16$
This isn't possible. ....Since square of a number is always $\geq 0$
Therefore, real factors of $x^{2} + 16$ do not exist.

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