Problem 123 of 7
Relate real and complex factorization for (x^2+1)(x^2+2x+2)(x-3).
Using a hint is okay. It just tells the trainer to give you a little more review.
Hidden until you reveal it.
distinguish linear and irreducible quadratic factors.
Hidden until you reveal it.
Distinguish linear factors over complexes from irreducible quadratic factors over reals.
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Your answer is equivalent to the expected form.
Walkthrough
Full solution stays hidden until you ask for it.
1. Factor over real numbers first.
2. Identify irreducible real quadratic factors.
3. Split those factors into complex conjugate linear factors.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Saying real factorization is invalid because complex factorization is more complete.