Problem 114 of 7
Compare real and complex factorizations of x^3-x^2+x-1.
Hints
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explain what additional complex factors reveal.
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Explain what additional factors or roots appear over complex numbers.
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Correct
Your answer is equivalent to the expected form.
Solution
Walkthrough
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1. Factor as far as possible over real numbers.
2. Split any negative-discriminant quadratic over complex numbers.
3. Compare the levels of factorization.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Saying complex factorization changes the polynomial.