Factoring over the Complex Numbers, Answer 2

Exercise 2.

Factor the polynomial

completely (a) over the real numbers, (b) over the complex numbers.

Answer.

We can first pull out an x term:

The polynomial has the roots by the quadratic formula. It is thus irreducible over the real numbers. Consequently, over the real numbers, the polynomial factors completely as

over the complex numbers, the polynomial factors completely into

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Helmut Knaust
Tue Jun 24 09:45:58 MDT 1997