Answer
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Step 1:I'll solve this step-by-step using the specified LaTeX formatting guidelines:
Step 2:: Examine the polynomial
The given polynomial is $$x^{2} + 5$$.
This is a quadratic expression with no linear term (the coefficient of x is 0).
Step 3:: Attempt to factor
To factor a quadratic, we typically look for two numbers that multiply to give the constant term and add to give the coefficient of x. However, in this case: - The constant term is 5 - There is no x term
Step 4:: Recognize the special case
x^{2} + 5$$ cannot be factored over the real numbers.
This is because: - 5 is a prime number - There are no real numbers that can be multiplied to produce 5 and create a perfect factorization
Step 5:: Conclusion
The polynomial $$x^{2} + 5$$ is irreducible over the real numbers.
It can only be factored in the complex number system.
Final Answer
It remains in its original form.
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