Problem 106 of 7
Compare real and complex factorizations of x^4+4.
Using a hint is okay. It just tells the trainer to give you a little more review.
Hidden until you reveal it.
explain why expression irreducible over reals factors over complexes.
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Expression must allow comparison of real versus complex factorization.
Enter your answer
Your answer is equivalent to the expected form.
Walkthrough
Full solution stays hidden until you ask for it.
1. Factor over the real numbers if possible.
2. Find complex roots or complex factors when real factors are unavailable.
3. Compare what changes when complex numbers are allowed.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Saying irreducible over the reals means unfactorable over complexes.